A127334 Numbers that are the sum of 7 consecutive primes.

58, 75, 95, 119, 143, 169, 197, 223, 251, 281, 311, 341, 371, 401, 431, 463, 493, 523, 559, 593, 625, 659, 689, 719, 757, 791, 827, 863, 905, 947, 991, 1027, 1063, 1099, 1139, 1171, 1211, 1247, 1281, 1313, 1351, 1395, 1441, 1479, 1519, 1561, 1603, 1643

Offset: 1

Author

Artur Jasinski, Jan 11 2007

Keywords

• nonn

Comments

a(n) = absolute value of coefficient of x^6 of the polynomial Product_{j=0..6} (x - prime(n+j)) of degree 7; the roots of this polynomial are prime(n), ..., prime(n+6).

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001043, A011974, A034961, A034963, A034964, A082246, A127333, A127335, A127336, A127337, A127338, A127339.

Programs

GAP

P:=Filtered([1..1000],IsPrime);; List([0..50],n->Sum([1+n..7+n],i->P[i])); # Muniru A Asiru, Apr 16 2018

Magma

[&+[ NthPrime(n+k): k in [0..6] ]: n in [1..70] ]; // Vincenzo Librandi, Apr 03 2011

Maple

seq(add(ithprime(i),i=n..6+n),n=1..50); # Muniru A Asiru, Apr 16 2018

Mathematica

a = {}; Do[AppendTo[a, Sum[Prime[x + n], {n, 0, 6}]], {x, 1, 50}]; a
Total/@Partition[Prime[Range[60]],7,1] (* Harvey P. Dale, May 14 2023 *)

PARI

{m=48;k=7;for(n=0,m-1,print1(a=sum(j=1,k,prime(n+j)),","))} \\ Klaus Brockhaus, Jan 13 2007

PARI

{m=48;k=7;for(n=1,m,print1(abs(polcoeff(prod(j=0,k-1,(x-prime(n+j))),k-1)),","))} \\ Klaus Brockhaus, Jan 13 2007

Python

from sympy import prime
def a(x): return sum(prime(x + n) for n in range(7))
print([a(i) for i in range(1, 50)]) # Indranil Ghosh, Mar 18 2017

Sage

BB = primes_first_n(62)
L = []
for i in range(55):
    L.append(sum(BB[i+j] for j in range(7)))
L
# Zerinvary Lajos, May 14 2007

Extensions

Edited by Klaus Brockhaus, Jan 13 2007