|
| |
|
|
A034964
|
|
Sums of five consecutive primes.
|
|
24
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
