A068235 - OEIS

%I #13 Apr 03 2023 10:36:10

%S 11,467,1499,16763,260339,2003387,7722419,20221283,927161471,

%T 4284484931,7355362139,84805717127,478527373859,2046207697631,

%U 7302359785151,21104656617827,21104656617827

%N a(n) is the smallest prime p such that p and the next n-1 primes are all == 11 (mod 12).

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

%C a(18) > 4*10^14. - _Giovanni Resta_, Aug 04 2013

%H The Prime Glossary, <a href="https://t5k.org/glossary/page.php?sort=DicksonsConjecture">Dickson's conjecture</a>

%t For[i=n=1, True, Null, For[j=0, j<n&&Mod[Prime[i+j], 12]==11, j++, Null]; If[j==n, Print[Prime[i]]; n++, i++ ]]

%o (PARI) {i=n=1; while(1,j=0; while(j<n&&prime(i+j)%12==11,j++); if(j==n,print(prime(i)); n++,i++))}

%Y Cf. A068227, A068228, A068229, A040117, A068231, A068232, A068233, A068234.

%K more,nice,nonn

%O 1,1

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

%E Edited by _Dean Hickerson_, Mar 06 2002

%E More terms from _Giovanni Resta_, Feb 18 2006

%E a(16)-a(17) from _Giovanni Resta_, Aug 04 2013