[1] http://www.mathpages.com/home/dseal.htm. Accessed: 2022-06-15.
[2] Digit reversal sums leading to palindromes. http://www.mathpages.com/home/kmath004/ kmath004.htm. Accessed: 2022-06-15.
[3] K. Alladi and P. Erdo˝s. On an additive arithmetic function. Pacific J. Math., 71(2):275–294, 1977.
[4] G. E. Andrews and G. Simay. Parity palindrome compositions. Integers, 21:A85, 2021.
[5] T. M. Apostol. Introduction to analytic number theory. Springer Science & Business Media, 1998.
[6] W. D. Banks. Every natural number is the sum of forty-nine palindromes. Integers, 16:A3, 2016.
[7] W. D. Banks, D. N. Hart, and M. Sakata. Almost all palindromes are composite. Math. Res. Lett., 11(5–6):853–868, 2004.
[8] J. Bayless and D. Klyve. Reciprocal sums as a knowledge metric: theory, computation, and perfect numbers. Amer. Math. Monthly, 120(9):822–831, 2013.
[9] K. A. Brown, S. M. Dunn, and J. Harrington. Arithmetic progressions in the polygonal numbers. Integers, 12:A43, 2012.
[10] P. Bundschuh and R. Bundschuh. Distribution of fibonacci and lucas numbers modulo 3k. Fibonacci Quart., 49(3):201–210, 2011.
[11] S. A. Burr. On moduli for which the fibonacci sequence contains a complete system of residues. Fibonacci Quart., 9(5):497–504, 1971.
[12] Y.-G. Chen and C.-H. Lei. Arithmetic progressions in the least positive reduced residue systems. J. Number Theory, 190:303–310, 2018.
[13] J. Cilleruelo, F. Luca, and L. Baxter. Every positive integer is a sum of three palindromes. Math. Comp., 87(314):3023–3055, 2018.
[14] J. Cilleruelo, F. Luca, and I. E. Shparlinski. Power values of palindromes. J. Comb. Number Theory, 1(2):101–107, 2009.
[15] J. Cilleruelo, R. Tesoro, and F. Luca. Palindromes in linear recurrence sequences. Monatsh. Math., 171(3–4):433–442, 2013.
[16] H. Davenport. The higher arithmetic: An introduction to the theory of numbers. Cambridge University Press, 1999.
[17] R. Dolbeau. The p196 mpi page. http://www.dolbeau.name/dolbeau/p196/p196.html. Accessed: 2021-09-19.
[18] H. Gabai and D. Coogan. On palindromes and palindromic primes. Math. Mag., 42(5):252–254, 1969.
[19] M. Gardner. The Magic Numbers of Dr. Matrix. Prometheus Books, 1985.
[20] B. Green and T. Tao. The primes contain arbitrarily long arithmetic progressions. Ann. of Math. (2), 167(2):481–547, 2008.
[21] L. Hajdu, M. Szikszai, and V. Ziegler. On arithmetic progressions in lucas sequences. https://arxiv.org/abs/1703.06722, 2017.
[22] M. Harminc. The existence of palindromic multiples. Matematicke´ obzory, 32:37–42, 1989. (Slovak).
[23] M. Harminc and R. Sota´k. Palindromic numbers in arithmetic progressions. Fibonacci Quart., 36(3):259–261, 1998.
[24] V. E. Hoggatt and M. Bicknell. Palindromic compositions. Fibonacci Quart., 13(4):350–356, 1975.
[25] M. Just. Compositions that are palindromic modulo m. https://arxiv.org/abs/2102.00996, 2021.
[26] L. F. Klosinski and D. C. Smolarski. On the reversing of digits. Math. Mag., 42(4):208–210, 1969.
[27] I. Korec. Palindromic squares of nonpalindromic numbers in various number system bases. Matem- aticke´ obzory, 33:35–43, 1989.
[28] I. Korec. Palindromic squares for various number system bases. Math. Slovaca, 41(3):261–276, 1991.
[29] F. Luca. Palindromes in lucas sequences. Monatsh. Math., 138(3):209–223, 2003.
[30] N. H. McCoy. Introduction to Modern Algebra. Allyn and Bacon, Inc., 1975.
[31] Y. Nishiyama. Numerical palindromes and the 196 problem. Int. J. Pure Appl. Math., 80(3):375–384, 2012.
[32] P. Phunphayap and P. Pongsriiam. Reciprocal sum of palindromes. J. Integer Seq., 22(8):Art. 19.8.6, 2019.
[33] P. Pollack. Palindromic sums of proper divisors. Integers, 15:A13, 2015.
[34] P. Pongsriiam. Longest arithmetic progressions in reduced residue systems. J. of Number Theory, 183:309–325, 2018.
[35] P. Pongsriiam. Longest arithmetic progressions of palindromes. J. Number Theory, 222:362–375, 2021.
[36] P. Pongsriiam and K. Subwattanachai. Exact formulas for the number of palindromes up to a given positive integer. Int. J. Math. Comput. Sci., 14(1):27–46, 2019.
[37] K. C. Rabi and A. Algoud. Staircase palindromic polynomials. https://arxiv.org/abs/2012. 15663, 2020.
[38] A. Rajasekaran, J. Shallit, and T. Smith. Sums of palindromes: an approach via automata. In 35th Symposium on Theoretical Aspects of Computer Science, volume 96 of LIPIcs. Leibniz Int. Proc. Inform., pages Art. No. 54, 12. Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2018.
[39] A. Restrepo and L. P. Chaco´n. On the period of sums of discrete periodic signals. IEEE Signal Processing Lett., 5(7):164–166, 1998.
[40] A. Schinzel. A class of polynomials. Math. Slovaca, 41(3):295–298, 1991.
[41] L. Spiegelhofer. A digit reversal property for an analogue of stern’s sequence. J. Integer Seq., 20(10):Art. 17.10.8, 2017.
[42] T. Tao and V. H. Vu. Additive combinatorics, volume 105. Cambridge University Press, 2006.
[43] Terry Tao. Is there an arbitrarily long arithmetic progression whose members are palindromes? (answer). MathOverflow. URL:http://mathoverflow.net/a/206162 (visited on 2021-11-07).
[44] C. W. Trigg. Palindromes by addition. Math. Mag., 40(1):26–28, 1967.
[45] D. Tsai. Natural numbers satisfying an unusual property. Su¯ gaku Seminar, 57(11):35–36, 2018. (Japanese).
[46] D. Tsai. The fundamental period of a periodic phenomenon pertaining to v-palindromic numbers. https://arxiv.org/abs/2103.00989, 2021. (Integers, to appear).
[47] D. Tsai. The invariance of the type of a v-palindrome. https://arxiv.org/abs/2112.13376, 2021.
[48] D. Tsai. A recurring pattern in natural numbers of a certain property. Integers, 21:A32, 2021.
[49] D. Tsai. Repeated concatenations in residue classes. https://arxiv.org/abs/2109.01798, 2021.
[50] D. Tsai. v-palindromes: an analogy to the palindromes. https://arxiv.org/abs/2111.10211, 2021.
[51] P. P. Vaidyanathan. Ramanujan sums in the context of signal processing–part i: Fundamentals. IEEE Trans. Signal Process., 62(16):4145–4157, 2014.
[52] P. P. Vaidyanathan. Ramanujan sums in the context of signal processing–part ii: Fir representations and applications. IEEE Trans. Signal Process., 62(16):4158–4172, 2014.
[53] P. P. Vaidyanathan and S. Tenneti. Srinivasa ramanujan and signal-processing problems. Phil. Trans. R. Soc. A, 378(2163), 2019.
[54] Wikipedia contributors. Lychrel number — Wikipedia, the free encyclopedia. https://en. wikipedia.org/w/index.php?title=Lychrel_number&oldid=1091177582, 2022. [Online; ac- cessed 8-July-2022].