A393322 Prime numbers prime(i) such that reversal(prime(i)) = prime(reversal(i)).

2, 3, 5, 7, 11, 37, 73, 143787341, 11853735811

Offset

1,1

Comments

Prime numbers prime(i) with the mirror property (see the Pomerance, Spicer article in Links, section 1. and 6.).

Links

Table of n, a(n) for n=1..9.

Carl Pomerance and Chris Spicer, Proof of the Sheldon Conjecture, The American Mathematical Monthly, September 2019, 126(8), 688-698.

Formula

a(n) = prime(A069469(n)) = A000040(A069469(n)).

Example

For prime(12) = 37: reversal(37) = prime(reversal(12)) which is true because 73 = prime(21), thus 37 is a term.

Mathematica

q[k_]:=IntegerReverse[Prime[k]]==Prime[IntegerReverse[k]]; Prime[Select[Range[10^5], q]] (* James C. McMahon, Feb 16 2026 *)

Crossrefs

Cf. A000040, A000720, A046941, A069469.

Sequence in context: A334026 A140561 A140553 * A195337 A141500 A215162

Adjacent sequences: A393319 A393320 A393321 * A393323 A393324 A393325

Keyword

nonn,base,more

Author

Ctibor O. Zizka, Feb 11 2026

Status

approved