A364679 - OEIS

A364679

Least increasing sequence of semiprimes with alternating parity such that a(n-1) + a(n) is a semiprime, with a(1)=4.

4, 21, 34, 35, 58, 65, 94, 111, 142, 145, 146, 155, 166, 169, 202, 205, 206, 209, 218, 219, 226, 247, 254, 265, 278, 287, 302, 309, 314, 319, 362, 391, 394, 395, 398, 415, 454, 469, 482, 497, 514, 527, 554, 565, 626, 629, 634, 679, 706, 731, 734, 763, 766, 771, 794, 849, 862, 865, 866, 869, 926

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OFFSET

1,1

LINKS

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

EXAMPLE

a(3) = 34 because a(2) = 21 (odd), the next even semiprimes are 22 = 2 * 11, 26 = 2 * 13 and 34 = 2 * 17, but 21 + 22 = 45 = 3^2 * 5 and 21 + 26 = 47 are not semiprimes and 21 + 34 = 55 = 5 * 11 is a semiprime.

MAPLE

R:= 4: x:= 4: y:= 3: count:= 0:

while count < 100 do

y:= y+2;

if numtheory:-bigomega(y) = 2 and numtheory:-bigomega(x+y) = 2 then

R:= R, y; count:= count+1; x:= y; y:= x-1

od:

MATHEMATICA

s = {k1 = 4}; Do[k = k1 + 1; While[2 != PrimeOmega[k] || 2 != PrimeOmega[k1 + k],

k = k + 2]; AppendTo[s, k1 = k], {200}]; s

CROSSREFS

Cf. A001358, A254923.