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 A034953 Triangular numbers (A000217) with prime indices. 47
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 The infinite sum over the reciprocals is given by 2*A179119. - Wolfdieter Lang, Jul 10 2019 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Triangular Number FORMULA a(n) = A000217(A000040(n)). - Omar E. Pol, Jul 27 2009 MATHEMATICA t[n_] := n(n + 1)/2; Table[t[Prime[n]], {n, 44}] (* Robert G. Wilson v, Aug 12 2004 *) (#(# + 1))/2&/@Prime[Range[50]] (* Harvey P. Dale, Feb 27 2012 *) PROG (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 CROSSREFS Cf. A000217, A034954, A034955, A011756, A179119, A195678. Sequence in context: A285563 A285543 A318396 * A086737 A063834 A139117 Adjacent sequences:  A034950 A034951 A034952 * A034954 A034955 A034956 KEYWORD nonn,easy AUTHOR Patrick De Geest, Oct 15 1998 STATUS approved

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Last modified October 20 07:33 EDT 2019. Contains 328252 sequences. (Running on oeis4.)