A298763 -id:A298763 - cp's OEIS frontend

A381061 First of six consecutive primes such that sum of any five terms is prime.

9733, 970217, 3218471, 5241937, 5691893, 8445251, 8788079, 11268497, 11881901, 16697419, 19604623, 22057961, 22926473, 26027723, 26939197, 38187463, 38938153, 39901963, 45190247, 52489691, 54887597, 58296113, 61909753, 62686369, 68142289, 69567359, 69799033, 72085687, 72973723, 79517741, 82464511

Offset: 1

Zak Seidov and Robert Israel, Feb 12 2025

nonn

			a(2) = 970217 is a term because 970217, 970219, 970231, 970237, 970247, 970259 are six consecutive primes such that the sums of five of the six are
    970217 + 970219 + 970231 + 970237 + 970247 = 4851151
    970217 + 970219 + 970231 + 970237 + 970259 = 4851163
    970217 + 970219 + 970231 + 970247 + 970259 = 4851173
    970217 + 970219 + 970237 + 970247 + 970259 = 4851179
    970217 + 970231 + 970237 + 970247 + 970259 = 4851191
    970219 + 970231 + 970237 + 970247 + 970259 = 4851193
which are all prime.

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..500 from _Robert Israel_)

Cf. A298763, A381062.

P:= [2,3,5,7,11,13]: S:= convert(P,`+`);
R:= NULL: count:= 0:
while count < 40 do
  p:= nextprime(P[6]);
  S:= S + p - P[1];
  P:= [op(P[2..6]),p];
  if andmap(t -> isprime(S-t), P) then
    R:= R,P[1]; count:= count+1;
  fi
od:
R;

from sympy import isprime, nextprime
from itertools import combinations, islice
def agen(): # generator of terms
    P = [2, 3, 5, 7, 11, 13]
    while True:
        if all(isprime(sum(c)) for c in combinations(P, 5)):
            yield P[0]
        P = P[1:] + [nextprime(P[-1])]
print(list(islice(agen(), 7))) # Michael S. Branicky, Feb 12 2025

A381062 a(n) is the first prime p such that the sum of any 2n-1 of the 2n consecutive primes starting with p is prime.

Original entry on oeis.org

2, 19, 9733, 69398759

Offset: 1

Robert Israel, Feb 12 2025

			a(2) = 19 because the sum of any 3 of the 4 primes 19, 23, 29, 31 is prime:
  19 + 23 + 29 = 71
  19 + 23 + 31 = 73
  19 + 29 + 31 = 79
  23 + 29 + 31 = 83 are all prime, and 19 is the first prime that works.

Cf. A298763, A381061.

f:= proc(n) local P,S,p,i;
  P:= [0,seq(ithprime(i),i=1..2*n-1)]:
  S:= convert(P,`+`);
  do
    p:= nextprime(P[-1]);
    S:= S + p - P[1];
    P:= [op(P[2..-1]),p];
    if andmap(t -> isprime(S-t),P) then return P[1] fi
  od
end proc:
map(f, [$1..4]);

cp's OEIS Frontend

A381061 First of six consecutive primes such that sum of any five terms is prime.

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A381062 a(n) is the first prime p such that the sum of any 2n-1 of the 2n consecutive primes starting with p is prime.

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cp's OEIS Frontend

A381061 First of six consecutive primes such that sum of any five terms is prime.

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Maple

Python

A381062 a(n) is the first prime p such that the sum of any 2*n-1 of the 2*n consecutive primes starting with p is prime.

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A381062 a(n) is the first prime p such that the sum of any 2n-1 of the 2n consecutive primes starting with p is prime.