A033447 Initial prime in set of 4 consecutive primes with common difference 12.

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

Offset: 1

Author

Jeff Burch

Keywords

• nonn

Comments

From Zak Seidov, Sep 30 2014: (Start)

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

• Zak Seidov, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to primes in arithmetic progressions

Crossrefs

Analogous sequences (start of CPAP-4 with common difference in square brackets): A033451 [6], this sequence [12], A033448 [18], A052242 [24], A052243 [30], A058252 [36], A058323 [42], A067388 [48], A259224 [54], A210683 [60].

Subsequence of A052188 and of A248085. - Zak Seidov, Jun 27 2015

Also subsequence of A054800: start of a CPAP-4, any common difference.

Programs

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]] (* Jean-François Alcover, Jun 28 2012 *)
Transpose[Select[Partition[Prime[Range[160000]],4,1],Union[ Differences[#]] =={12}&]][[1]] (* Harvey P. Dale, Jun 17 2014 *)

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(o-g", "); n--||break); o=q-g); o-g} \\ Can be used as next(p)=A033447(1, p+1) to get the next term, e.g.:
p=0; A033447_vec=vector(30,i,p=A033447(1,p+1)) \\ M. F. Hasler, Oct 26 2018

Extensions

More terms from Labos Elemer, Jan 31 2000

Definition clarified by Harvey P. Dale, Jun 17 2014