A340575 a(n) is the least prime p such that the product of 2*n-1 consecutive primes starting with p is divisible by the sum of those same primes, or 0 if there is no such prime.

2, 2, 3, 5, 5, 3, 2, 11, 7, 7, 5, 2, 3, 0, 3, 7, 11, 7, 31, 2, 2, 2, 5, 13, 3, 3, 2, 71, 2, 3, 31, 109, 71, 7, 3, 0, 2, 59, 2, 17, 3, 5, 61, 0, 29, 17, 41, 29, 5, 3, 5, 3, 11, 79, 0, 41, 3, 11, 5, 5, 5, 37, 37, 59, 13, 3, 3, 3, 31, 31, 61, 2, 2, 3, 2, 2, 2, 23, 2, 5, 11, 5, 7, 2, 5, 5, 67, 5, 0

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

For n=4, the product of 2*4-1 = 7 primes starting with a(4) = 5 is 5*7*11*13*17*19*23 which is divisible by 5+7+11+13+17+19+23 = 95 = 5*19.

Maple

plow:= n -> n*(ln(n)+ln(ln(n))-1):
phi:= n -> n*(ln(n)+ln(ln(n))):
f:= proc(n) local i, k, m, q;
  m:= 2*n-1;
  for k from 0 do
    if mul(ithprime(k+i), i=1..2*n-1) mod add(ithprime(k+i), i=1..2*n-1) = 0 then return ithprime(k+1) fi;
    if k >= 5 and is(m*phi(k+m-1) < plow(k)^2) then return 0 fi;
  od;
end proc:
map(f, [$1..100]);

Crossrefs

Sequence in context: A284114 A323480 A330404 * A139171 A329570 A279724

Adjacent sequences: A340572 A340573 A340574 * A340576 A340577 A340578

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jan 19 2021

Status

approved