A008507 Number of odd composite numbers less than n-th odd prime.

0, 0, 0, 1, 1, 2, 2, 3, 5, 5, 7, 8, 8, 9, 11, 13, 13, 15, 16, 16, 18, 19, 21, 24, 25, 25, 26, 26, 27, 33, 34, 36, 36, 40, 40, 42, 44, 45, 47, 49, 49, 53, 53, 54, 54, 59, 64, 65, 65, 66, 68, 68, 72, 74, 76, 78, 78, 80, 81, 81, 85, 91, 92, 92, 93, 99, 101, 105, 105, 106, 108, 111, 113, 115, 116, 118

Offset: 1

Author

Gary Findley (chfindley(AT)alpha.nlu.edu)

Keywords

• nonn

Comments

a(n) = A067076(n) - n + 1. - Vincenzo Librandi, Feb 02 2013

For n>=4, a(n) = k+1, where A000217(j) is the smallest triangular number such that A000217(j) - A033286(n+1) also is a triangular number, i.e., A000217(k). Example n=29, a(29) = 27: A033286(30) = 3390, A000217(86) = 3741. 3741-3390 = 351 = A000217(26); k=26, 26+1 = 27. - Bob Selcoe, Apr 12 2016

Crossrefs

Cf. A067076.

Cf. A000040 (prime numbers), A000217 (triangular numbers), A033286 (n*prime(n)).

Partial sums of A100820.

Formula

[(Odd Primes - 1)/2] - n for n > 0, or A005097(n) - A000027(n). For example, A005097(1) - A000027(1) = 1 - 1 = 0, A005097(2) - A000027(2) = 2 - 2 = 0, A005097(9) - A000027(9) = 14 - 9 = 5. - William A. Tedeschi, Apr 25 2008

Extensions

More terms from David W. Wilson, Jan 13 2000