A068234 a(n) is the smallest prime p such that p and the next n-1 primes are all == 5 (mod 12).

5, 509, 4397, 42509, 647417, 647417, 1248869, 13175609, 234946997, 1039154933, 7114719473, 32021552837, 32021552837, 1237381737257, 2904797643617, 2904797643617, 2904797643617

Offset

1,1

Comments

Dickson's conjecture implies that a(n) exists for all n.

a(18) > 4*10^14. - Giovanni Resta, Aug 04 2013

Links

Table of n, a(n) for n=1..17.

The Prime Glossary, Dickson's conjecture

Mathematica

For[i=n=1, True, Null, For[j=0, j<n&&Mod[Prime[i+j], 12]==5, j++, Null]; If[j==n, Print[Prime[i]]; n++, i++ ]]
Module[{nn=129*10^5, pr5}, pr5=Table[If[Mod[Prime[n], 12]==5, 1, 0], {n, nn}]; Prime[ #]&/@Flatten[Table[SequencePosition[pr5, PadRight[{}, k, 1], 1], {k, 9}], 1][[All, 1]]] (* The program generates the first 9 terms of the sequence. *) (* Harvey P. Dale, Feb 02 2022 *)

Prog

(PARI) {i=n=1; while(1, j=0; while(j<n&&prime(i+j)%12==5, j++); if(j==n, print(prime(i)); n++, i++))}

Crossrefs

Cf. A068227, A068228, A068229, A040117, A068231, A068232, A068233, A068235.

Sequence in context: A083151 A128682 A228093 * A012741 A317821 A318428

Adjacent sequences: A068231 A068232 A068233 * A068235 A068236 A068237

Keyword

nice,nonn

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu), Feb 22 2002

Extensions

Edited by Dean Hickerson, Mar 06 2002

More terms from Giovanni Resta, Feb 18 2006

Status

approved