A068232 a(n) is the smallest prime p such that p and the next n-1 primes are all == 1 (mod 12).

13, 661, 8317, 12829, 586153, 1081417, 7790917, 7790917, 370861009, 370861009, 370861009, 5637496849, 289391626057, 469257742237, 628337233501, 84424712545429, 155494152002017, 341821313785729

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..18.

The Prime Glossary, Dickson's conjecture

Mathematica

For[i=n=1, True, Null, For[j=0, j<n&&Mod[Prime[i+j], 12]==1, j++, Null]; If[j==n, Print[Prime[i]]; n++, i++]
Module[{p12=Mod[Prime[Range[2*10^7]], 12]}, Table[Prime[ SequencePosition[ p12, PadRight[ {}, n, 1], 1][[All, 1]]], {n, 11}]]//Flatten (* Requires Mathematica version 10 or later *) (* The program generates the first 11 terms of the sequence *) (* Harvey P. Dale, Dec 24 2020 *)

Prog

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

Crossrefs

Cf. A068227, A068228, A068229, A040117, A068231, A068233, A068234, A068235.

Sequence in context: A362898 A316331 A217380 * A363864 A092547 A298951

Adjacent sequences: A068229 A068230 A068231 * A068233 A068234 A068235

Keyword

nice,nonn

Author

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

Extensions

Edited by Dean Hickerson, Mar 06 2002

a(12)-a(15) from Giovanni Resta, Feb 18 2006

a(16)-a(18) from Giovanni Resta, Aug 04 2013

Status

approved