A185999 Automorphic semiprimes: semiprimes, sp, such that sp is the k-th semiprime and sp ends in k.

291, 24502749, 36627829, 3547310731, 4721984179, 461808766011

Offset: 1

Author

Jonathan Vos Post & Robert G. Wilson v, Feb 24 2011

Keywords

• hard
• nonn
• base

Comments

Analogy, this sequence is to semiprimes (A001358) as A046883 is to the primes (A000040) or as A035383 is to the squares (A000290) among many others.

Links

• Index entries for sequences related to automorphic numbers

Crossrefs

Cf. A001358, A046883, A046883, A186000.

Programs

Mathematica

nextSemiPrime[n_] := Block[{k = n + 1}, While[ Plus @@ Last /@ FactorInteger@ k != 2, k++]; k]; c = 1; k = 4; lst = {}; While[k < 8100000000, If[ Mod[k, 10^Floor[1 + Log10@ c]] == c, AppendTo[lst, k]; Print[{c, k}]]; c++; k = nextSemiPrime@ k]; lst
These terms can be crosschecked by: SemiPrimePi[n_] := Sum[ PrimePi[n/Prime@ i] -i + 1, {i, PrimePi@ Sqrt@ n}]

Extensions

a(6) from Donovan Johnson, Mar 03 2011