[seqfan] Pairwise sums are all semiprimes. II

zak seidov zakseidov at yahoo.com
Sat Jun 12 20:15:55 CEST 2010


A1

a(1) = 1; for n>1, a(n) = smallest number of the form 4k+1 and a(n) > a(n-1) such that the pairwise sums of elements are all semiprimes.

1, 9, 13, 25, 133, 193, 18673, 57313, 1032313, 4387273
Or, for i<>J, (a(i)+a(j)/2 are primes.


A2

a(1) = 3; for n>1, a(n) = smallest number of the form 4k+3 and a(n) > a(n-1) such that the pairwise sums of elements are all semiprimes.

3, 7, 19, 55, 139, 859, 2119, 112999, 333679, 10040119, 15363619, 548687179

Are A1 and A2 finite? More terms?

Thanks,
Zak



      




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