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%I #13 Apr 03 2023 10:36:10
%S 7,199,199,32443,180799,180799,4338787,84885631,472798219,1786054267,
%T 6024282871,64791932287,592175010019,6265824724519,7816088451907,
%U 24660781037467
%N a(n) is the smallest prime p such that p and the next n-1 primes are all == 7 (mod 12).
%C Dickson's conjecture implies that a(n) exists for all n.
%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]==7, 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==7,j++); if(j==n,print(prime(i)); n++,i++))}
%Y Cf. A068227, A068228, A068229, A040117, A068231, A068232, A068234, A068235.
%K 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) from _Giovanni Resta_, Aug 04 2013