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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

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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