A305887 The least increasing sequence of numbers where all pairwise sums are semiprimes, with a(1)=4.

4, 5, 10, 29, 173, 249, 19073, 71489, 1166789, 3800333, 7021253, 15920129, 84551600693, 224223772673

Offset: 1

Author

Zak Seidov, Jun 14 2018

Keywords

• nonn
• more

Comments

All terms > 10 are congruent to {3, 9} mod 10.

Triangle of resulting semiprimes begins:

9

14, 15

33, 34, 39

177, 178, 183, 202

Crossrefs

Cf. A001358, A116656, A164979, A181620.

Programs

Mathematica

Nest[Append[#, Block[{k = Last[#] + 1}, While[! AllTrue[#, PrimeOmega[k + #] == 2 &], k++]; k]] &, {4}, 7] (* Michael De Vlieger, Jun 14 2018 *)

Extensions

a(13) from Giovanni Resta, Jun 14 2018

a(14) from Jinyuan Wang, May 29 2025