A269850 a(n) = number of integers k <= n for which prime(k+1)-prime(k) is a multiple of three.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 10, 10, 11, 12, 12, 12, 12, 12, 12, 13, 14, 14, 14, 14, 15, 15, 15, 16, 17, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 22, 23, 23, 24, 24, 24, 24, 24, 24, 24, 24, 25, 25, 26, 26, 26, 26, 26, 27

Offset

1,11

Comments

a(n) = number of terms of A270190 <= n, the least monotonic left inverse of A270190.

See comments at A269364.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Terence Tao, Biases between consecutive primes, blog entry March 14, 2016

Formula

Other identities. For all n >= 1:

a(A270190(n)) = n.

Mathematica

Table[Count[Select[Range@ 125, Divisible[Prime[# + 1] - Prime@ #, 3] &], k_ /; k <= n], {n, 91}] (* Michael De Vlieger, Mar 17 2016 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A269850 (LEFTINV-LEASTMONO 1 1 A270190))
(PARI) a(n) = sum(k=1, n, ((prime(k+1) - prime(k)) % 3) == 0); \\ Michel Marcus, Mar 18 2016

Crossrefs

Cf. A270190, A269849, A269364.

Sequence in context: A035450 A234537 A029126 * A036054 A029102 A241086

Adjacent sequences: A269847 A269848 A269849 * A269851 A269852 A269853

Keyword

nonn

Author

Antti Karttunen, Mar 16 2016

Status

approved