A100821 a(n) = 1 if prime(n) + 2 = prime(n+1), otherwise 0.

0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0

Offset

1,1

Comments

Same as A062301 except for starting point.

a(n)=1 iff prime(n) is the smaller of a pair of twin primes, else a(n)=0. This sequence can be derived from the sequence b(n)=1 iff n and n+2 are both prime, else b(n)=0. This latter sequence has as its inverse Moebius transform the sequence c(n) = the number of distinct factors of n which are the smaller of a pair of twin primes. For example, c(15)=2 because 15 is divisible by 3 and 5, each of which is the smaller of a pair of twin primes. - Jonathan Vos Post, Jan 07 2005

Links

Table of n, a(n) for n=1..105.

Formula

a(n) = A062301(n+1) = 1 - A100810(n).

Mathematica

Table[If[Prime[n] + 2 == Prime[n + 1], 1, 0], {n, 120}] (* Ray Chandler, Jan 09 2005 *)

Crossrefs

Sequence in context: A359372 A327861 A131929 * A139689 A204175 A343173

Adjacent sequences: A100818 A100819 A100820 * A100822 A100823 A100824

Keyword

easy,nonn

Author

Giovanni Teofilatto, Jan 06 2005

Extensions

Corrected and extended by Ray Chandler, Jan 09 2005

Status

approved