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%I #15 Mar 25 2017 20:28:19
%S 2424,2462,2466,2642,2646,2664,2666,4242,4246,4264,4624,4626,4662,
%T 4666,6246,6264,6266,6424,6426,6462,6466,6626,6642,6646,6662,6664
%N Decimal concatenations of the quadruples (d1,d2,d3,d4) with elements in {2,4,6} for which there exists a prime p >= 5 such that the differences between the 5 consecutive primes starting with p are (d1,d2,d3,d4).
%e 4624 corresponds to the quadruple (4,6,2,4). It is in the sequence because the 5 consecutive primes 1597, 1601, 1607, 1609 and 1613 have differences (4,6,2,4).
%t With[{k = 4}, FromDigits /@ Select[Tuples[Range[2, 6, 2], k], Function[m, Count[Range[k, 10^k], 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[3, 2000], 4, 1], Max@ # <= 6 &] (* _Giovanni Resta_, Mar 25 2017 *)
%Y The least primes corresponding to the quadruples are in A078866. The same primes, in increasing order, are in A078867. The sequences of primes corresponding to the 26 difference patterns are in A022006 (for 2424), A022007 (for 4242) and A078946-A078970. The similarly defined quintuples are in A078870. Cf. A001223.
%K fini,full,base,nonn
%O 1,1
%A _Labos Elemer_, Dec 19 2002
%E Edited by _Dean Hickerson_, Dec 20 2002
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