A342035 Numbers k such that both bigomega(k)+sopfr(k) and bigomega(k)+sopfr(k)+k are prime.

2, 6, 18, 24, 26, 30, 38, 56, 72, 90, 104, 120, 152, 158, 162, 174, 206, 218, 288, 294, 318, 342, 344, 350, 354, 360, 378, 408, 446, 458, 486, 510, 522, 534, 558, 690, 696, 698, 726, 776, 792, 824, 878, 894, 910, 936, 990, 992, 1016, 1056, 1078, 1098, 1152, 1170, 1184, 1256, 1278, 1286, 1330

Offset

1,1

Comments

Numbers k such that A001222(k)+A001414(k) and A001222(k)+A001414(k)+k are prime.

All terms are even.

Semiprimes in the sequence are 2*p where p is in the intersection of A023200 and A023209.

Links

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

Example

a(4) = 24 = 2^3*3 is in the sequence because A001222(24) = 3+1 = 4, A001414(24) = 3*2+3 = 9, and 4+9 = 13 and 4+9+24 = 37 are prime.

Maple

filter:= proc(n) local k, v;
  v:= add(k[2]*(1+k[1]), k = ifactors(n)[2]);
  isprime(v) and isprime(n+v)
end proc:
select(filter, [seq(i, i=2..2000, 2)]);

Crossrefs

Cf. A001222, A001414, A023200, A023209.

Sequence in context: A127257 A050832 A300600 * A168149 A275990 A220142

Adjacent sequences: A342032 A342033 A342034 * A342036 A342037 A342038

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Feb 25 2021

Status

approved