login
A265915
Primes that are sum of 5 consecutive primes congruent to 1 mod 6.
0
107, 191, 239, 281, 419, 461, 683, 947, 1103, 1301, 1451, 1511, 1571, 1637, 1697, 1979, 2039, 2099, 2213, 2837, 2903, 2969, 3167, 3299, 3461, 3533, 3659, 3803, 3947, 4019, 4241, 4523, 4721, 5051, 5099, 5153, 5309, 5693, 5867, 6053, 6131, 6287, 6353, 6491, 6959, 7079, 7151, 7211, 7433, 7517
OFFSET
1,1
COMMENTS
Or, primes that are sum of 5 consecutive terms of A002476.
First primes that are sum of 7 consecutive terms of A002476: 211, 271, 331, 457, 523, 727, 883, 1327, 1399, 1567.
First primes that are sum of 11 consecutive terms of A002476: 719, 827, 1049, 1163, 1499, 1619, 1733, 1973, 2087, 3023.
First primes that are sum of 5 and also of 11 consecutive terms of A002476: 11579, 25367, 37253, 49937, 50411, 59183, 69827, 92717.
EXAMPLE
a(1) = 107 = A000040(28) = A002476(1)+...+A002476(5) = 7+13+19+31+37,
a(2) = 143 = A000040(34) = A002476(2)+...+A002476(6) = 13+19+31+37+43.
MATHEMATICA
Select[Total /@ Partition[Select[Range[7, 2000, 6], PrimeQ], 5, 1], PrimeQ]
Select[Total/@Partition[Select[Prime[Range[300]], Mod[#, 6]==1&], 5, 1], PrimeQ] (* Harvey P. Dale, Aug 26 2021 *)
PROG
(PARI) list(lim)=my(v=List(), u=[0, 7, 13, 19, 31], t=70); forprime(p=37, , if(p%6>1, next); t+=p-u[1]; if(t>=lim, return(Vec(v))); if(isprime(t), listput(v, t)); u=concat(u[2..5], p)) \\ Charles R Greathouse IV, Dec 18 2015
CROSSREFS
Sequence in context: A229570 A107215 A142142 * A210361 A250147 A142270
KEYWORD
nonn
AUTHOR
Zak Seidov, Dec 18 2015
STATUS
approved