A365861 - OEIS

A365861

a(1) = 4; for n > 1, a(n) is the first semiprime k not yet listed such that |k - a(n-1)| and k + a(n-1) are also semiprimes.

4, 10, 25, 21, 166, 51, 26, 65, 69, 118, 85, 34, 111, 115, 46, 95, 38, 77, 142, 93, 226, 9, 86, 35, 14, 129, 74, 49, 106, 15, 6, 209, 94, 39, 326, 91, 87, 122, 143, 58, 33, 82, 121, 146, 55, 22, 133, 158, 183, 298, 155, 62, 185, 134, 119, 262, 57, 178, 123, 218, 253, 249, 334, 201, 422, 169, 202

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OFFSET

1,1

COMMENTS

Conjecture: this is a permutation of A001358.

LINKS

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

EXAMPLE

a(3) = 25 because 25 = 5^2 is a semiprime, |a(2) - 25| = 15 = 3 * 5 and a(2) + 25 = 35 = 5 * 7 are semiprimes, and 25 is the first semiprime not already in the sequence for which this works.

MAPLE

R:= 4: a:= 4: S:= select(t -> numtheory:-bigomega(t)=2, [$6..1000]): found:= true:

for n from 2 to 100 while found do

found:= false;

for j from 1 to nops(S) do

b:=S[j];

if numtheory:-bigomega(abs(b-a)) = 2 and numtheory:-bigomega(a+b) = 2 then

R:= R, b; a:= b; found:= true; S:= subsop(j=NULL, S);

break

od od:

MATHEMATICA

s={m=4}; Do[n=6; While[MemberQ[s, n]|| {2, 2, 2} != PrimeOmega[{n, n-m, n+m}], n++];