A068575 -id:A068575 - cp's OEIS frontend

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

Felice Russo and Carlos Rivera

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

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

Index entries for sequences related to automorphic numbers

Cf. A067248, A068575, A075902, A046884.

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 *)

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

A067248 Numbers k such that the digits of prime(k) end in k.

Original entry on oeis.org

7, 9551, 303027, 440999, 968819, 5517973, 27737957, 93230839, 46492090901, 426836115943, 732382677641, 4895576080181, 77628540590583, 3475456543097857, 20396537622790811

Offset: 1

Joseph L. Pe, Feb 20 2002

There is no further term up to 115000000. - Farideh Firoozbakht, Jan 01 2007

a(13) > pi(10^15). - Donovan Johnson, May 08 2010

			Prime(968819) = 14968819 which ends in 968819, so 968819 is a term of the sequence.

Corresponding primes are in A046883.

Cf. A046883, A068575, A075902.

(* returns true if a ends with b, false otherwise *) f[a_, b_] := Module[{c, d, e, g, h, i, r}, r = False; c = ToString[a]; d = ToString[b]; e = StringLength[c]; g = StringPosition[c, d]; h = Length[g]; If[h > 0, i = g[[h]]; If[i[[2]] == e, r = True]]; r]; Do[If[f[Prime[n], n], Print[n]], {n, 1, 10^6}]

a(6) from Zak Seidov, Sep 27 2002
a(7)-a(8) from Farideh Firoozbakht, Jan 01 2007
a(9)-a(12) from Donovan Johnson, May 08 2010
a(13)-a(14) from Chai Wah Wu, Apr 05 2021
a(15) from Chai Wah Wu, Apr 07 2021

A103174 Numbers k with increasing digits such that the digits of k appear among the digits of the k-th prime number.

Original entry on oeis.org

7, 5789, 234567, 345679

Offset: 1

Labos Elemer, Feb 28 2005

We assume digits of k are in increasing order. No terms < 10^7.

Sequence is complete. - Giovanni Resta, Apr 29 2017

			n: {7, 5789, 234567, 345679}
prime(n): {17, 57089, 3264857, 4956733}

Cf. A080794, A068575, A075902.

Select[Rest@ Union[FromDigits /@ Subsets@ Range@ 9], SubsetQ @@ IntegerDigits@ {Prime@#, #} &] (* Giovanni Resta, Apr 29 2017 *)

Definition edited by Giovanni Resta, May 01 2017

cp's OEIS Frontend

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

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A067248 Numbers k such that the digits of prime(k) end in k.

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A103174 Numbers k with increasing digits such that the digits of k appear among the digits of the k-th prime number.

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