

A269850


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


5



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
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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 IntSeqlibrary)
(define A269850 (LEFTINVLEASTMONO 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



