A290572 Least number that is the start of a gap of size n between numbers that are either prime or twice a prime (A001751).

2, 11, 7, 67, 53, 47, 514, 401, 317, 181, 467, 526, 1069, 2819, 1262, 3142, 1382, 1913, 1327, 4178, 2477, 9697, 8123, 8329, 3274, 11213, 21031, 5119, 16382, 13063, 20446, 44417, 22193, 37747, 12854, 46957, 35617, 63863, 48679, 20809, 76166, 39251, 110359, 59282, 136898, 212923, 143006

Offset: 1

Author

Bobby Jacobs and Robert G. Wilson v, Aug 06 2017

Keywords

• nonn

Comments

Numbers that are less than any later number are recorded in A290488.

Examples

			a(1) is  2 since  3 -  2 = 1;
a(2) is 11 since 13 - 11 = 2;
a(3) is  7 since 10 -  7 = 3;
a(4) is 67 since 71 - 67 = 4; etc.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..261
• Robert G. Wilson v, Table of n, a(n) for n = 0..290, or 0 if no such value is known.

Crossrefs

Cf. A001751, A002386, A290488, A290489.

Programs

Mathematica

nxt[n_] := Block[{k = n +1}, While[ !PrimeQ[k] && !PrimeQ[k/2], k++]; k]; p = 2; q = 3; t[_] = 0; While[p < 215000, d = q - p; If[ t[d] == 0, t[d] = p]; p = q; q = nxt@ q]; t@# & /@ Range@ 47