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A367855
The slowest increasing sequence of semiprimes such that a(n-1) + a(n) is prime.
1
4, 9, 10, 21, 22, 25, 34, 39, 58, 69, 82, 85, 94, 129, 134, 143, 194, 203, 206, 213, 218, 221, 278, 291, 302, 305, 314, 327, 334, 339, 362, 365, 386, 411, 446, 473, 566, 597, 626, 633, 674, 687, 694, 745, 766, 793, 1018, 1081, 1126, 1141, 1198, 1219, 1402, 1417, 1486, 1513, 1654, 1689, 1718, 1731
OFFSET
1,1
COMMENTS
a(2*n) is odd and a(2*n-1) is twice a prime where n is a positive integer. - David A. Corneth, Dec 03 2023
LINKS
EXAMPLE
a(4) = 21 because a(3) = 10, 21 = 3 * 7 is a semiprime > 10, 10 + 21 = 31 is prime, and no smaller semiprime > 10 works.
MAPLE
R:= 4: s:= 4:
for count from 2 to 100 do
for t from s+1 by 2 do
if isprime(s+t) and numtheory:-bigomega(t) = 2 then
R:= R, t; s:= t; break
fi
od
od:
R;
MATHEMATICA
s = {q = 4}; Do[p = q + 1; While[ PrimeOmega[p] != 2, p = p + 2]; AppendTo[s, q = p], {120}]; s
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Dec 02 2023
STATUS
approved