A265915 - OEIS

A265915

Primes that are sum of 5 consecutive primes congruent to 1 mod 6.

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

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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.

LINKS

Table of n, a(n) for n=1..50.

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

Cf. A000040, A002476.

Sequence in context: A229570 A107215 A142142 * A210361 A250147 A142270

Adjacent sequences: A265912 A265913 A265914 * A265916 A265917 A265918

KEYWORD

nonn

AUTHOR

Zak Seidov, Dec 18 2015

STATUS

approved