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A339438 Composite numbers k such that k + A339436(k) is prime. 1
6, 10, 14, 15, 20, 21, 24, 26, 33, 34, 35, 38, 40, 44, 46, 51, 52, 55, 57, 58, 63, 65, 74, 76, 85, 86, 88, 90, 92, 93, 96, 111, 117, 118, 123, 124, 135, 136, 141, 143, 145, 147, 150, 153, 155, 158, 161, 164, 166, 172, 177, 178, 180, 184, 185, 194, 198, 201, 203, 205, 206, 207, 208, 209, 215, 221 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If n = p_1 * ... * p_m with primes p_i <= p_{i+1}, then p_1 + p_1*p_2 + ... + p_1*p_2*...*p_m + p2*...*p_m + ... + p_m is prime.

LINKS

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

EXAMPLE

a(5)=20 is a term because 20=2*2*5 and 2+2*2+2*2*5+2*5+5 = 41 is prime.

MAPLE

filter:= proc(n) local L, m;

  L:= sort(map(t -> t[1]$t[2], ifactors(n)[2]));

  m:= nops(L);

  if m=1 then return false fi;

  isprime(n + add(mul(L[i], i=1..j)+mul(L[i], i=j+1..m), j=1..m-1))

end proc:

select(filter, [$4..300]);

CROSSREFS

Includes A088709.

Cf. A339436, A339437.

Sequence in context: A063763 A115956 A066073 * A268376 A067582 A229153

Adjacent sequences:  A339435 A339436 A339437 * A339439 A339440 A339441

KEYWORD

nonn

AUTHOR

J. M. Bergot and Robert Israel, Dec 04 2020

STATUS

approved

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Last modified March 7 10:38 EST 2021. Contains 341869 sequences. (Running on oeis4.)