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A068232
a(n) is the smallest prime p such that p and the next n-1 primes are all == 1 (mod 12).
8
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.
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++))}
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