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

0,6

Links

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

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A265133 A064506 A082774 * A248333 A303905 A341904

Adjacent sequences: A074236 A074237 A074238 * A074240 A074241 A074242

Keyword

easy,nonn

Author

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

Status

approved