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

1,6

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

Links

Table of n, a(n) for n=1..76.

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

Crossrefs

Cf. A067076.

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

Partial sums of A100820.

Sequence in context: A089366 A113827 A033189 * A318683 A028364 A239482

Adjacent sequences: A008504 A008505 A008506 * A008508 A008509 A008510

Keyword

nonn

Author

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

Extensions

More terms from David W. Wilson, Jan 13 2000

Status

approved