A127334 - OEIS

%I #46 May 14 2023 13:13:02

%S 58,75,95,119,143,169,197,223,251,281,311,341,371,401,431,463,493,523,

%T 559,593,625,659,689,719,757,791,827,863,905,947,991,1027,1063,1099,

%U 1139,1171,1211,1247,1281,1313,1351,1395,1441,1479,1519,1561,1603,1643

%N Numbers that are the sum of 7 consecutive primes.

%C 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).

%H Muniru A Asiru, <a href="/A127334/b127334.txt">Table of n, a(n) for n = 1..1000</a>

%p seq(add(ithprime(i),i=n..6+n),n=1..50); # _Muniru A Asiru_, Apr 16 2018

%t a = {}; Do[AppendTo[a, Sum[Prime[x + n], {n, 0, 6}]], {x, 1, 50}]; a

%t Total/@Partition[Prime[Range[60]],7,1] (* _Harvey P. Dale_, May 14 2023 *)

%o (PARI) {m=48;k=7;for(n=0,m-1,print1(a=sum(j=1,k,prime(n+j)),","))} \\ _Klaus Brockhaus_, Jan 13 2007

%o (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

%o (Sage)

%o BB = primes_first_n(62)

%o L = []

%o for i in range(55):

%o     L.append(sum(BB[i+j] for j in range(7)))

%o L

%o # _Zerinvary Lajos_, May 14 2007

%o (Magma) [&+[ NthPrime(n+k): k in [0..6] ]: n in [1..70] ]; // _Vincenzo Librandi_, Apr 03 2011

%o (Python)

%o from sympy import prime

%o def a(x): return sum(prime(x + n) for n in range(7))

%o print([a(i) for i in range(1, 50)]) # _Indranil Ghosh_, Mar 18 2017

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

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

%K nonn

%O 1,1

%A _Artur Jasinski_, Jan 11 2007

%E Edited by _Klaus Brockhaus_, Jan 13 2007