A082462 Let chi(k) = 1 if prime(k+1) - prime(k) = 2, = 0 otherwise; sequence gives a(n) = Sum_{k <= n} chi(k).

0, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21

Offset

1,3

Comments

a(n) is the number of lesser twin primes <= prime(n). - Sean A. Irvine, Dec 09 2025

Links

Table of n, a(n) for n=1..78.

Formula

a(n)=A071538(A000040(n)). [From R. J. Mathar, Oct 06 2008]

Example

  n   p  D  a(n) (p=prime(n), D = prime(n+1)-prime(n))
  1   2  1   0
  2   3  2   1
  3   5  2   2
  4   7  4   2
  5  11  2   3
  6  13  4   3

Crossrefs

Cf. A000040, A001223, A001359.

Sequence in context: A001462 A377862 A357021 * A276581 A005041 A030530

Adjacent sequences: A082459 A082460 A082461 * A082463 A082464 A082465

Keyword

nonn

Author

Artemario Tadeu Medeiros da Silva (artemario(AT)uol.com.br), Apr 26 2003

Status

approved