A074239 Related to cumulative number of non-twin primes.

0, 0, 0, 1, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 11, 12, 13, 14, 15, 16, 16, 17, 17, 18, 19, 20, 21, 21, 22, 22, 23, 24, 25, 26, 27, 27, 28, 28, 29, 29, 30, 31, 32, 32, 33, 34, 34, 35, 36, 37, 38, 38, 39, 40, 40, 41, 42, 43, 43, 44, 45, 46, 47, 47, 48, 49, 50

Offset: 0

Author

Rudi Huysmans (rudi.huysmans(AT)pandora.be), Sep 18 2002

Keywords

• easy
• nonn

Links

• Robert Israel and Paul Nanninga, Table of n, a(n) for n = 0..10000 (terms up to a(100) from Paul Nanninga)

Crossrefs

Cf. A065091 (odd primes), A007510 (non-twin primes).

Programs

Maple

N:= 100: # to get a(0) to a(N)
P:= [seq(ithprime(i),i=2..N+2)]:
ListTools:-PartialSums([0,seq(`if`(P[i]-P[i-1]=2,0,1),i=2..N+1)]); # Robert Israel, May 13 2016

Mathematica

Accumulate@ Table[If[Prime@ n - Prime[n - 1] == 2, 0, 1], {n, 2, 120}] - 1 (* Michael De Vlieger, May 13 2016, after Robert Israel *)

PARI

op(n) = prime(n+1);
lista(nn) = {my(x=0); for (n=1, nn, print1(x, ", "); if ((op(n+1) - op(n)) > 2, x++););} \\ Michel Marcus, May 13 2016

Formula

Take the sequence of odd primes op(n); set a(0) = 0; if op(n+1)-op(n)=2 a(n+1) = a(n), if op(n+1)-op(n) > 2 a(n+1) = a(n) + 1.