A269849 a(n) = number of integers k <= n for which prime(k+1)-prime(k) is not a multiple of three.

1, 2, 3, 4, 5, 6, 7, 8, 8, 9, 9, 10, 11, 12, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 18, 19, 20, 21, 22, 23, 24, 24, 25, 26, 27, 27, 27, 28, 28, 28, 29, 30, 31, 32, 33, 33, 33, 34, 35, 36, 36, 37, 38, 38, 38, 38, 39, 39, 40, 41, 42, 43, 44, 45, 46, 47, 47, 48, 49, 50, 50, 51, 51, 51, 52, 52, 53, 54, 55, 56, 57, 58, 59, 59, 60

Offset

1,2

Comments

a(n) = number of terms of A270189 <= n, the least monotonic left inverse of A270189.

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(A270189(n)) = n.

Mathematica

Table[Count[Select[Range@ 125, Mod[Prime[# + 1] - Prime@ #, 3] != 0 &], k_ /; k <= n], {n, 85}] (* Michael De Vlieger, Mar 17 2016 *)
Accumulate[If[Mod[#, 3]==0, 0, 1]&/@Differences[Prime[Range[90]]]] (* Harvey P. Dale, Apr 15 2024 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A269849 (LEFTINV-LEASTMONO 1 1 A270189))
(PARI) a(n) = sum(k=1, n, ((prime(k+1) - prime(k)) % 3) != 0); \\ Michel Marcus, Mar 18 2016

Crossrefs

Cf. A270189, A269850, A269362, A269364.

Sequence in context: A327708 A079631 A347623 * A228881 A252373 A245338

Adjacent sequences: A269846 A269847 A269848 * A269850 A269851 A269852

Keyword

nonn,changed

Author

Antti Karttunen, Mar 16 2016

Status

approved