A034964 Sums of five consecutive primes.

28, 39, 53, 67, 83, 101, 119, 139, 161, 181, 199, 221, 243, 263, 287, 311, 331, 351, 373, 395, 421, 449, 473, 497, 517, 533, 559, 587, 617, 647, 683, 707, 733, 759, 787, 811, 839, 863, 891, 917, 941, 961, 991, 1023, 1057, 1089, 1123, 1151, 1169, 1193

Offset

1,1

Comments

Except for the first term, all terms are odd. - Alonso del Arte, Dec 30 2011

References

Owen O'Shea and Underwood Dudley, The Magic Numbers of the Professor, Mathematical Association of America (2007), p. 62

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{i=n..n+4} prime(i). - Wesley Ivan Hurt, Sep 14 2014

Example

a(1) = prime(1+0) + prime(1+1) + prime(1+2) + prime(1+3) + prime(1+4) = 2 + 3 + 5 + 7 + 11 = 28.
a(2) = prime(2+0) + prime(2+1) + prime(2+2) + prime(2+3) + prime(2+4) = 3 + 5 + 7 + 11 + 13 = 39.

Maple

A034964:=n->add(ithprime(i), i=n..n+4): seq(A034964(n), n=1..50); # Wesley Ivan Hurt, Sep 14 2014

Mathematica

Plus@@@Partition[Prime[Range[100]], 5, 1] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2010 *)

Prog

(Sage)
BB = primes_first_n(60)
L = []
for i in range(55):
    L.append(BB[i]+BB[i+1]+BB[i+2]+BB[i+3]+BB[i+4])
L # Zerinvary Lajos, May 14 2007
(Magma) [&+[ NthPrime(n+k): k in [0..4] ]: n in [1..100] ]; // Vincenzo Librandi, Apr 03 2011
(PARI) a(n) = sum(k=n, n+4, prime(k)); \\ Michel Marcus, Sep 03 2016
(PARI) first(n) = {my(psum = 28, pr = List([2, 3, 5, 7, 11]), res = List([28])); for(i=2, n, psum -= pr[1]; listpop(pr, 1); listput(pr, nextprime(pr[4] + 1)); psum += pr[5]; listput(res, psum)); res} \\ David A. Corneth, Oct 14 2017

Crossrefs

Cf. A000040, A001043, A011974, A034707.

Cf. A131686 (sums of five consecutive squares of primes).

Sequence in context: A096430 A204822 A179166 * A195897 A109798 A216594

Adjacent sequences: A034961 A034962 A034963 * A034965 A034966 A034967

Keyword

nonn,easy

Author

Patrick De Geest, Oct 15 1998

Extensions

Offset changed to 1 by Joerg Arndt, Sep 04 2016

Status

approved