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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 (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

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 !! (n-1)

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

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Last modified April 24 00:44 EDT 2014. Contains 240947 sequences.