login
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
OFFSET
1,1
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)
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 *)
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(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
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.
Sequence in context: A296370 A206509 A033446 * A203667 A210059 A236892
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Labos Elemer, Jan 31 2000
Definition clarified by Harvey P. Dale, Jun 17 2014
STATUS
approved