login
Primes p such that there exists k such that p = prime(k) + prime(k+2) + prime(k+4) + prime(k+6) + prime(k+8).
4

%I #29 Sep 08 2022 08:45:05

%S 71,181,223,307,353,379,401,541,641,757,1109,1277,1327,1511,1607,1777,

%T 1801,1861,1889,2333,2393,2423,2713,2791,2837,2897,2927,2953,3041,

%U 3067,3121,3391,3617,3821,3943,4013,4153,4241,4327,4523,4549,4621,5113,5233

%N Primes p such that there exists k such that p = prime(k) + prime(k+2) + prime(k+4) + prime(k+6) + prime(k+8).

%C Equivalently, primes that are the sum of 5 alternate primes. - _Muniru A Asiru_, Feb 12 2018

%H Muniru A Asiru, <a href="/A068364/b068364.txt">Table of n, a(n) for n = 1..10000</a>

%e 71 is prime and equal to 3 + 7 + 13 + 19 + 29, so 71 is a term.

%p p:=ithprime: select(isprime, [seq(sum(p(2*i-1+k), i=1..5), k=0..180)]); # _Muniru A Asiru_, Feb 12 2018

%t Select[Total /@ Table[Prime[n + m], {n, 200}, {m, 0, 8, 2}], PrimeQ] (* _Harvey P. Dale_, May 02 2011 *)

%o (GAP) P:=Filtered([1..5000], IsPrime);; Filtered(List([0..200], k-> Sum([1..5], i -> P[2*i-1+k])), IsPrime); # _Muniru A Asiru_, Feb 12 2018

%o (Magma) [p: k in [1..200] | IsPrime(p) where p is &+[NthPrime(k+2*i): i in [0..4]]]; // _Bruno Berselli_, Feb 13 2018

%Y Cf. A068363.

%K nonn,easy

%O 1,1

%A _Benoit Cloitre_, Feb 28 2002