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

Author

Felice Russo and Carlos Rivera

Keywords

• base
• nice
• nonn

Comments

a(13) > 10^15. - Donovan Johnson, Mar 26 2010

Examples

			p(7)=17, p(9551)=99551, p(303027)=4303027, p(440999)=6440999, p(968819)=14968819, p(5517973)=95517973.
		

Links

• Index entries for sequences related to automorphic numbers

Crossrefs

Cf. A067248, A068575, A075902, A046884.

Programs

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