A058323 Initial prime in set of 4 consecutive primes with common gap 42.

23921257, 32611897, 33215597, 35650007, 44201617, 49945837, 51616717, 70350487, 70687937, 74816107, 78789707, 86066047, 99641917, 101568287, 129031187, 146922077, 149568217, 151779517, 153921017, 156793337, 162881627

Offset: 1

Author

Harvey P. Dale, Dec 12 2000

Keywords

• nonn

Comments

All a(n) == 7 mod 10. - Robert Israel, May 13 2015

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 (with differences in square brackets): A033451 [6], A033447 [12], A033448 [18], A052242 [24], A052243 [30], A058252 [36].

Programs

Mathematica

d[x_] := Prime[x+1]-Prime[x] {k1=42, k2=42, k3=42} k=0 Do[If[Equal[d[n], k1]&&Equal[d[n+1], k2]&& Equal[d[n+2], k3], k=k+1; Print[{k, n, Prime[n], Prime[n+1], Prime[n+2], Prime[n+3]}]], {n, 1, 10000000}]
Transpose[Select[Partition[Prime[Range[9000000]], 4, 1], Union[Differences[#]]=={42}&]][[1]] (* Vincenzo Librandi, Jun 21 2015 *)

Extensions

More terms from Labos Elemer, Jan 11 2002

Definition corrected by Robert Israel, May 13 2015

Definition edited by Zak Seidov, Jun 21 2015

Offset changed 0 -> 1 by Zak Seidov, Jun 21 2015