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A069469 Numbers k such that prime(reversal(k)) = reversal(prime(k)). Ignore leading 0's.

%I A069469 #42 Jun 13 2025 08:21:20
%S A069469 1,2,3,4,5,12,21,8114118,535252535
%N A069469 Numbers k such that prime(reversal(k)) = reversal(prime(k)). Ignore leading 0's.
%C A069469 For an arithmetical function f, call the arguments n such that f(reverse(n)) = reverse(f(n)) the "palinpoints" of f. This sequence is the sequence of palinpoints of f(n) = prime(n).
%C A069469 These are all the palinpoints of prime(n) not exceeding 10^7. There are more (535252535 is known to be a term, but it is not known whether it is the next one).
%C A069469 Contains all n such that n and prime(n) are both palindromes, i.e. A046942. Heuristically, we would expect there to be infinitely many of these, but they will be rare: the number of them with at most d digits may be on the order of sqrt(d). - _Robert Israel_, May 30 2016
%C A069469 a(10) > 10^9. - _Giovanni Resta_, Apr 13 2017
%H A069469 Jessie Byrnes, Chris Spicer and Alyssa Turnquist, <a href="https://doi.org/10.4169/mathhorizons.23.2.12">The Sheldon Conjecture</a>. Math Horizons, Vol. 23, No. 2 (November 2015), pp. 12-15 (4 pages); <a href="https://www.jstor.org/stable/10.4169/mathhorizons.23.2.12">alternate link</a>.
%H A069469 Carl Pomerance and Chris Spicer, <a href="https://doi.org/10.1080/00029890.2019.1626672">Proof of the Sheldon Conjecture</a>, The American Mathematical Monthly, September 2019, 126(8), 688-698; <a href="https://math.dartmouth.edu/~carlp/sheldon02132019.pdf">alternate link</a>.
%e A069469 Let f(n) = prime(n). Then f(21) = 73, f(12) = 37, so f(reverse(21)) = reverse(f(21)). Therefore 21 belongs to the sequence.
%t A069469 rev[n_] := FromDigits[Reverse[IntegerDigits[n]]]; f[n_] := Prime[n]; Select[Range[10^5], f[rev[ # ]] == rev[f[ # ]] &]
%Y A069469 Cf. A000040, A002113, A075807, A046942.
%K A069469 base,nonn
%O A069469 1,2
%A A069469 _Joseph L. Pe_, Apr 15 2002
%E A069469 a(8) added by _Ivan Neretin_, May 30 2016
%E A069469 a(9) from _Giovanni Resta_, Apr 13 2017