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

1, 2, 3, 4, 5, 12, 21, 8114118, 535252535

Offset: 1

Author

Joseph L. Pe, Apr 15 2002

Keywords

• base
• nonn

Comments

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).

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).

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

a(10) > 10^9. - Giovanni Resta, Apr 13 2017

Examples

			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.
		

Links

• Jessie Byrnes, Chris Spicer and Alyssa Turnquist, The Sheldon Conjecture. Math Horizons, Vol. 23, No. 2 (November 2015), pp. 12-15 (4 pages); alternate link.
• Carl Pomerance and Chris Spicer, Proof of the Sheldon Conjecture, The American Mathematical Monthly, September 2019, 126(8), 688-698; alternate link.

Crossrefs

Cf. A000040, A002113, A075807, A046942.

Programs

Mathematica

rev[n_] := FromDigits[Reverse[IntegerDigits[n]]]; f[n_] := Prime[n]; Select[Range[10^5], f[rev[ # ]] == rev[f[ # ]] &]

Extensions

a(8) added by Ivan Neretin, May 30 2016

a(9) from Giovanni Resta, Apr 13 2017