A288022 Prime p1 of consecutive primes p1, p2, where p2 - p1 = 6, and p1, p2 are in different decades.

47, 157, 167, 257, 367, 557, 587, 607, 647, 677, 727, 947, 977, 1097, 1117, 1187, 1217, 1367, 1657, 1747, 1777, 1907, 1987, 2207, 2287, 2417, 2467, 2677, 2837, 2897, 2957, 3307, 3407, 3607, 3617, 3637, 3727, 3797, 4007, 4357, 4457, 4507, 4597, 4657, 4937, 4987

Offset

1,1

Comments

The unit digits of the numbers in the sequence are 7's.

Number of terms < 10^k: 0, 0, 1, 13, 81, 565, 4027, 30422, 237715, ... - Muniru A Asiru, Jan 09 2018

Links

Muniru A Asiru, Table of n, a(n) for n = 1..10000

Example

47 is in the sequence since pair (47,53) is the first with difference 6 spanning a multiple of 10.

Maple

for n from 1 to 2000 do if [ithprime(n+1)-ithprime(n), ithprime(n) mod 5] = [6, 2] then print(ithprime(n)); fi; od; # Muniru A Asiru, Jan 19 2018

Mathematica

a288022[n_] := Map[Last, Select[Map[{NextPrime[#, 1], NextPrime[#, -1]}&, Range[10, n, 10]], First[#]-Last[#]==6&]]
a288022[3000] (* data *)

Prog

(GAP)
P:=Filtered([1..20000], IsPrime);
P1:=List(Filtered(Filtered(List([1..Length(P)-1], n->[P[n], P[n+1]]), i->i[2]-i[1]=6), j->j[1] mod 5=2), k->k[1]); # Muniru A Asiru, Jul 08 2017

Crossrefs

Cf. A001359, A023201, A023203, A031924, A031925, A031928, A046117, A046132, A158277, A158861, A160370, A160440, A160500, A287049, A287050, A060229, A288021, A288024.

Sequence in context: A142505 A047948 A142529 * A142634 A140641 A141994

Adjacent sequences: A288019 A288020 A288021 * A288023 A288024 A288025

Keyword

nonn

Author

Hartmut F. W. Hoft, Jun 04 2017

Status

approved