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Prime p1 of consecutive primes p1, p2, where p2 - p1 = 6, and p1, p2 are in different decades.
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%I #28 Jan 19 2018 07:34:24

%S 47,157,167,257,367,557,587,607,647,677,727,947,977,1097,1117,1187,

%T 1217,1367,1657,1747,1777,1907,1987,2207,2287,2417,2467,2677,2837,

%U 2897,2957,3307,3407,3607,3617,3637,3727,3797,4007,4357,4457,4507,4597,4657,4937,4987

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

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

%C Number of terms < 10^k: 0, 0, 1, 13, 81, 565, 4027, 30422, 237715, ... - _Muniru A Asiru_, Jan 09 2018

%H Muniru A Asiru, <a href="/A288022/b288022.txt">Table of n, a(n) for n = 1..10000</a>

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

%p 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

%t a288022[n_] := Map[Last, Select[Map[{NextPrime[#, 1], NextPrime[#, -1]}&, Range[10, n, 10]], First[#]-Last[#]==6&]]

%t a288022[3000] (* data *)

%o (GAP)

%o P:=Filtered([1..20000], IsPrime);

%o 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

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

%K nonn

%O 1,1

%A _Hartmut F. W. Hoft_, Jun 04 2017