A068232 - OEIS

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

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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