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A111208
Number of primes <= n-th triangular number.
9
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
0,3
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
FORMULA
a(n) = A000720(A000217(n)).
MATHEMATICA
Table[PrimePi[n*(n + 1)/2], {n, 0, 60}] (* Ray Chandler, Oct 31 2005 *)
PROG
(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
(Haskell)
a111208 n = length $ takeWhile (<= a000217 n) a000040_list
CROSSREFS
KEYWORD
nonn
AUTHOR
Giovanni Teofilatto, Oct 25 2005
EXTENSIONS
Extended by Ray Chandler and Alonso del Arte, Oct 31 2005
STATUS
approved