A078869 -id:A078869 - cp's OEIS frontend

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).

24246, 24626, 24662, 26424, 26426, 26462, 26466, 26642, 26646, 26664, 42424, 42462, 42466, 42646, 46246, 46264, 46266, 46626, 46662, 62462, 62642, 62646, 62664, 62666, 64242, 64246, 64264, 64624, 64626, 64662, 64666, 66264, 66266, 66424, 66462, 66466, 66626, 66646

Offset: 1

Labos Elemer, Dec 19 2002

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

Cf. A078868, A078869.

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

Edited by Dean Hickerson, Dec 20 2002

A078871 Decimal concatenations of the 6-tuples (d1,d2,d3,d4,d5,d6) with elements in {2,4,6} for which there exists a prime p >= 7 such that the differences between the 7 consecutive primes starting with p are (d1,d2,d3,d4,d5,d6).

Original entry on oeis.org

242462, 246264, 246266, 246626, 264242, 264246, 264264, 264626, 264666, 266424, 266466, 266646, 424626, 424662, 462462, 462642, 462646, 462664, 462666, 466264, 466266, 466626, 624626, 626424, 626426, 626462, 626466, 626642, 626646, 626664, 642462, 642466, 642646, 646246, 646264, 646266, 646626, 646662, 662642, 662646, 662664, 662666, 664246, 664626, 664662, 666264, 666266, 666462

Offset: 1

Labos Elemer, Dec 20 2002

			For 424662, the first 2 primes with the given differences are 37 and 25767877. For 646626, the least start prime is 6268957.

The least primes corresponding to the 6-tuples are in A078874. The same primes, in increasing order, are in A078875. The similarly defined quadruples and quintuples are in A078868 and A078870. Cf. A001223, A078869.

Edited by Dean Hickerson, Dec 21 2002

cp's OEIS Frontend

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).

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