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A034964
Sums of five consecutive primes.
25
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
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. A131686 (sums of five consecutive squares of primes).
Sequence in context: A096430 A204822 A179166 * A195897 A109798 A216594
KEYWORD
nonn,easy
AUTHOR
Patrick De Geest, Oct 15 1998
EXTENSIONS
Offset changed to 1 by Joerg Arndt, Sep 04 2016
STATUS
approved