

A034953


Triangular numbers (A000217) with prime indices.


37



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

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 2n1 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 = nth 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


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)). [From Omar E. Pol, Jul 27 2009]


MATHEMATICA

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]] (* 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 !! (n1)
a034953_list = map a000217 a000040_list
 Reinhard Zumkeller, Sep 23 2011


CROSSREFS

Cf. A000217, A034954, A034955, A011756, A195678.
Sequence in context: A076971 A103529 A185378 * A086737 A063834 A139117
Adjacent sequences: A034950 A034951 A034952 * A034954 A034955 A034956


KEYWORD

nonn,easy


AUTHOR

Patrick De Geest, Oct 15 1998.


STATUS

approved



