A373891 Number of primes less than prime(n) having the same difference between consecutive primes as prime(n).

0, 0, 1, 0, 2, 1, 3, 2, 0, 4, 1, 3, 5, 4, 2, 3, 6, 4, 5, 7, 5, 6, 6, 0, 7, 8, 8, 9, 9, 0, 10, 7, 10, 0, 11, 8, 9, 11, 10, 11, 12, 1, 13, 12, 14, 0, 1, 13, 15, 14, 12, 16, 2, 13, 14, 15, 17, 16, 15, 18, 3, 1, 16, 19, 17, 2, 17, 4, 20, 18, 18, 1, 19, 20, 19, 21, 2, 20, 3, 5

Offset: 1

Author

Ilya Gutkovskiy, Jun 21 2024

Keywords

• nonn

Examples

			a(7) = 3 because A001223(7) = 2 and also A001223(2) = A001223(3) = A001223(5) = 2.
		

Links

• Index entries for primes, gaps between

Crossrefs

Cf. A000040, A001223, A274121.

Programs

Mathematica

Table[Length[Select[Range[n - 1], Prime[# + 1] - Prime[#] == Prime[n + 1] - Prime[n] &]], {n, 80}]

PARI

a(n) = my(vp = primes(n+1), dvp = vector(#vp-1, k, vp[k+1]-vp[k])); sum(i=1, #dvp-1, dvp[i] == dvp[#dvp]); \\ Michel Marcus, Jun 27 2024

Formula

a(n) = |{j < n : A001223(j) = A001223(n)}|.

a(n) = A274121(n) - 1.