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A034953
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Triangular numbers (A000217) with prime indices.
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36
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3, 6, 15, 28, 66, 91, 153, 190, 276, 435, 496, 703, 861, 946, 1128, 1431, 1770, 1891, 2278, 2556, 2701, 3160, 3486, 4005, 4753, 5151, 5356, 5778, 5995, 6441, 8128, 8646, 9453, 9730, 11175, 11476, 12403, 13366, 14028, 15051, 16110, 16471, 18336, 18721
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OFFSET
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1,1
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COMMENTS
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The following sequences (allowing offset of first term) all appear to have the same parity: A034953, triangular numbers with prime indices; A054269, length of period of continued fraction for sqrt(p), p prime; A082749, difference between the sum of next prime(n) natural numbers and the sum of next n primes; A006254, numbers n such that 2n-1 is prime; A067076, 2n+3 is a prime. - Jeremy Gardiner, Sep 10 2004
Given a rectangular prism with sides 1, p, p^2 for p = n-th prime (n>1), the area of the six sides divided by the volume gives a remainder which is 4*a(n). - J. M. Bergot, Sep 12 2011
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Triangular Number
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FORMULA
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a(n) = A000217(A000040(n)). [From Omar E. Pol, Jul 27 2009]
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MATHEMATICA
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t[n_] := n(n + 1)/2; Table[ t[ Prime[ n]], {n, 44}] (from Robert G. Wilson v Aug 12 2004)
(#(#+1))/2&/@Prime[Range[50]] (* From Harvey P. Dale, Feb 27 2012 *)
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PROG
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(PARI) forprime(p=2, 1e3, print1(binomial(p+1, 2)", ")) \\ Charles R Greathouse IV, Jul 19 2011
(PARI) apply(n->binomial(n+1, 2), primes(100)) \\ Charles R Greathouse IV, Jun 04 2013
(Haskell)
a034953 n = a034953_list !! (n-1)
a034953_list = map a000217 a000040_list
-- Reinhard Zumkeller, Sep 23 2011
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CROSSREFS
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Cf. A000217, A034954, A034955, A011756, A195678.
Sequence in context: A076971 A103529 A185378 * A086737 A063834 A139117
Adjacent sequences: A034950 A034951 A034952 * A034954 A034955 A034956
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KEYWORD
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nonn,easy
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AUTHOR
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Patrick De Geest, Oct 15 1998.
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STATUS
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approved
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