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

Author

Patrick De Geest, Oct 15 1998

Keywords

• nonn
• easy

Comments

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

Examples

			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.
		

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

Crossrefs

Cf. A000040, A001043, A011974, A034707.

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

Programs

Magma

[&+[ NthPrime(n+k): k in [0..4] ]: n in [1..100] ]; // Vincenzo Librandi, Apr 03 2011

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 *)

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

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

Formula

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

Extensions

Offset changed to 1 by Joerg Arndt, Sep 04 2016