

A033447


Initial prime in set of 4 consecutive primes with common difference 12.


23



111497, 258527, 286777, 318407, 332767, 341827, 358447, 439787, 473887, 480737, 495377, 634187, 647417, 658367, 663857, 703837, 732497, 816317, 819787, 827767, 843067, 862307, 937777, 970457, 970537, 1001267, 1012147, 1032727, 1052707, 1055827, 1104307, 1117877, 1164817, 1165837
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OFFSET

1,1


COMMENTS

All terms are == {7, 17} mod 30. There is no set of 5 consecutive primes in arithmetic progression with common difference 12 (because a(n)+48 is always divisible by 5).
Minimal first difference a(n+1)a(n) = 40, and this occurs first at a(709) = 26930767, a(11357) = 655389367 and a(23339) = 1510368877; all a(n) are == 7 mod 30. (End)


LINKS



MATHEMATICA

A033447 = Reap[For[p = 2, p < 1100000, p = NextPrime[p], p2 = NextPrime[p]; If[p2  p == 12, p3 = NextPrime[p2]; If[p3  p2 == 12, p4 = NextPrime[p3]; If[p4  p3 == 12, Sow[p]]]]]][[2, 1]] (* JeanFrançois Alcover, Jun 28 2012 *)
Transpose[Select[Partition[Prime[Range[160000]], 4, 1], Union[ Differences[#]] =={12}&]][[1]] (* Harvey P. Dale, Jun 17 2014 *)


PROG

(PARI) A033447(n, p=2, show_all=1, g=12, c, o)={forprime(q=p+1, , if(p+g!=p=q, next, q!=o+2*g, c=2, c++>3, show_all&& print1(og", "); nbreak); o=qg); og} \\ Can be used as next(p)=A033447(1, p+1) to get the next term, e.g.:


CROSSREFS

Also subsequence of A054800: start of a CPAP4, any common difference.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



