A078870 - OEIS

A078870

Decimal concatenations of the 38 quintuples (d1,d2,d3,d4,d5) with elements in {2,4,6} for which there exists a prime p >= 7 such that the differences between the 6 consecutive primes starting with p are (d1,d2,d3,d4,d5).

%I #12 Mar 25 2017 20:28:26

%S 24246,24626,24662,26424,26426,26462,26466,26642,26646,26664,42424,

%T 42462,42466,42646,46246,46264,46266,46626,46662,62462,62642,62646,

%U 62664,62666,64242,64246,64264,64624,64626,64662,64666,66264,66266,66424,66462,66466,66626,66646

%N Decimal concatenations of the 38 quintuples (d1,d2,d3,d4,d5) with elements in {2,4,6} for which there exists a prime p >= 7 such that the differences between the 6 consecutive primes starting with p are (d1,d2,d3,d4,d5).

%e 66646 is in the sequence because 3301, 3307, 3313, 3319, 3323 and 3329 are consecutive primes with differences (6,6,6,4,6).

%t With[{k = 5}, FromDigits /@ Select[Tuples[Range[2, 6, 2], k], Function[m, Count[Range[k - 1, 10^4], n_ /; Times @@ Boole@ Map[PrimeQ, Prime@ n + Accumulate@ m] == 1] > 0]]] (* _Michael De Vlieger_, Mar 25 2017 *) (* or *)

%t FromDigits /@ Union@ Select[ Partition[ Differences@ Prime[Range[4, 9000]], 5, 1], Max@ # <= 6 &] (* _Giovanni Resta_, Mar 25 2017 *)

%Y Cf. A078868, A078869.

%K fini,full,base,nonn

%O 1,1

%A _Labos Elemer_, Dec 19 2002

%E Edited by _Dean Hickerson_, Dec 20 2002