cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A046883 Automorphic primes: primes p such that p is k-th prime and p ends in k.

This page as a plain text file.
%I A046883 #42 Mar 18 2025 12:18:22
%S A046883 17,99551,4303027,6440999,14968819,95517973,527737957,1893230839,
%T A046883 1246492090901,12426836115943,21732382677641,154895576080181,
%U A046883 2677628540590583,133475456543097857,820396537622790811
%N A046883 Automorphic primes: primes p such that p is k-th prime and p ends in k.
%C A046883 a(13) > 10^15. - _Donovan Johnson_, Mar 26 2010
%H A046883 <a href="/index/Ar#automorphic">Index entries for sequences related to automorphic numbers</a>
%e A046883 p(7)=17, p(9551)=99551, p(303027)=4303027, p(440999)=6440999, p(968819)=14968819, p(5517973)=95517973.
%t A046883 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 *)
%t A046883 fQ[n_]:=StringPosition[ToString[Prime[n]],ToString[n]][[1,2]]==
%t A046883 IntegerLength[Prime[n]]; Prime[Select[Range[1,5517973,2],fQ]]//Quiet (* _Ivan N. Ianakiev_, Apr 15 2022 *)
%t A046883 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 *)
%Y A046883 Cf. A067248, A068575, A075902, A046884.
%K A046883 base,nice,nonn
%O A046883 1,1
%A A046883 _Felice Russo_ and _Carlos Rivera_
%E A046883 One more term from _Zak Seidov_, Sep 27 2002
%E A046883 Corrected by _Lior Manor_, Oct 14 2002
%E A046883 a(7)-a(8) from _Robert G. Wilson v_, May 21 2004
%E A046883 a(9)-a(12) from _Donovan Johnson_, Mar 26 2010
%E A046883 a(13)-a(14) from _Chai Wah Wu_, Apr 05 2021
%E A046883 a(15) from _Chai Wah Wu_, Apr 07 2021