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Search: id:A111208
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| A111208 |
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Number of primes <= n-th triangular number. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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 Delarte (alonso.delarte(AT)gmail.com), Oct 31 2005
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,10000
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FORMULA
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a(n) = A000720(A000217(n)).
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MATHEMATICA
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Table[PrimePi[n*(n + 1)/2], {n, 0, 60}] (*Chandler*)
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PROGRAM
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(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); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Mar 10 2009]
(Other) sage: [prime_pi(binomial(n, 2)) for n in xrange(1, 63)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 06 2009]
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CROSSREFS
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Cf. A000720, A000217.
Sequence in context: A018649 A135676 A102701 this_sequence A085500 A155211 A010385
Adjacent sequences: A111205 A111206 A111207 this_sequence A111209 A111210 A111211
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KEYWORD
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nonn
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AUTHOR
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Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Oct 25 2005
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net) and Alonso Delarte (alonso.delarte(AT)gmail.com), Oct 31 2005
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