A046883 Automorphic primes: primes p such that p is k-th prime and p ends in k.
17, 99551, 4303027, 6440999, 14968819, 95517973, 527737957, 1893230839, 1246492090901, 12426836115943, 21732382677641, 154895576080181, 2677628540590583, 133475456543097857, 820396537622790811
Offset: 1
Examples
p(7)=17, p(9551)=99551, p(303027)=4303027, p(440999)=6440999, p(968819)=14968819, p(5517973)=95517973.
Programs
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Mathematica
Do[ If[ Mod[ Prime[n], 10^Ceiling[ Log[10, n]]] == n, Print[Prime[n]]], {n, 1, 100000000, 2}] (* Robert G. Wilson v, May 21 2004 *) (* fixed by Ivan N. Ianakiev, Apr 15 2022 *) fQ[n_]:=StringPosition[ToString[Prime[n]],ToString[n]][[1,2]]== IntegerLength[Prime[n]]; Prime[Select[Range[1,5517973,2],fQ]]//Quiet (* Ivan N. Ianakiev, Apr 15 2022 *) Select[Table[{n,Prime[n]},{n,552*10^4}],Mod[#[[2]],10^IntegerLength[#[[1]]]]==#[[1]]&][[;;,2]] (* The program generates the first six terms of the sequence. *) (* Harvey P. Dale, Mar 18 2025 *)
Extensions
One more term from Zak Seidov, Sep 27 2002
Corrected by Lior Manor, Oct 14 2002
a(7)-a(8) from Robert G. Wilson v, May 21 2004
a(9)-a(12) from Donovan Johnson, Mar 26 2010
a(13)-a(14) from Chai Wah Wu, Apr 05 2021
a(15) from Chai Wah Wu, Apr 07 2021
Comments