A111208 Number of primes <= n-th triangular number.

0, 0, 2, 3, 4, 6, 8, 9, 11, 14, 16, 18, 21, 24, 27, 30, 32, 36, 39, 42, 46, 50, 54, 58, 62, 66, 70, 74, 79, 84, 90, 94, 99, 102, 108, 114, 121, 126, 131, 137, 141, 149, 154, 160, 166, 174, 180, 188, 193, 200, 205, 216, 220, 226, 235, 242, 250, 259, 267, 274, 281, 290

Offset: 0

Author

Giovanni Teofilatto, Oct 25 2005

Keywords

• nonn

Comments

Only because of the case n = 2 is it necessary to say "<=", otherwise "<" would suffice. Except for the first two terms, there are no consecutive identical terms for n < 10000. A065382 gives differences between consecutive terms of this sequence. - Alonso del Arte, Oct 31 2005

Links

• Harry J. Smith, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000720, A000217.

Cf. A038107, A014085, A194189.

Programs

Haskell

a111208 n = length $ takeWhile (<= a000217 n) a000040_list
-- Reinhard Zumkeller, Nov 01 2011

Mathematica

Table[PrimePi[n*(n + 1)/2], {n, 0, 60}] (* Ray Chandler, Oct 31 2005 *)

PARI

{ allocatemem(932245000); default(primelimit, 4294965247); write("b111208.txt", 0, " ", 0); for (n = 1, 10000, t=n*(n + 1)/2; a=primepi(t); write("b111208.txt", n, " ", a); ) } \\ Harry J. Smith, Mar 10 2009

Sage

[prime_pi(binomial(n,2)) for n in range(1, 63)] # Zerinvary Lajos, Jun 06 2009

Formula

a(n) = A000720(A000217(n)).

Extensions

Extended by Ray Chandler and Alonso del Arte, Oct 31 2005