A133608 Numbers n such that the sum of digits of n-th semiprime equals sum of digits of n.

5, 6, 19, 40, 41, 42, 70, 71, 85, 89, 128, 148, 149, 166, 199, 246, 257, 271, 285, 327, 339, 346, 448, 449, 469, 484, 566, 592, 605, 617, 634, 643, 644, 676, 682, 694, 710, 713, 719, 740, 748, 751, 752, 753, 782, 793, 794, 797, 798, 815, 890, 901, 905, 961

Offset: 1

Author

Jonathan Vos Post, Dec 27 2007

Keywords

• base
• easy
• nonn
• less

Comments

This is to A033549 as semiprimes A001358 are to primes A000040.

Examples

			a(1) = 5 because semiprime(5) = 14, whose sum of digits is 5, the same as its index as a semiprime.
		

Crossrefs

Cf. A001358, A007953, A033549.

Programs

Mathematica

a = {}; c = 0; For[n = 4, n < 10000, n++, If[Sum[FactorInteger[n][[i, 2]], {i, 1, Length[FactorInteger[n]]}] == 2, c++; If[Plus @@ IntegerDigits[c] == Plus @@ IntegerDigits[n], AppendTo[a, c]]]]; a (* Stefan Steinerberger, Dec 29 2007 *)
SemiPrimePi[n_] := Sum[ PrimePi[n/Prime@i] - i + 1, {i, PrimePi@ Sqrt@n}]; SemiPrime[n_] := Block[{e = Floor[Log[2, n] + 1], a, b}, a = 2^e; Do[b = 2^p; While[SemiPrimePi@a < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; Select[Range@ 1000, fQ@# &] (* Robert G. Wilson v *)
nn=5000;With[{sp=Select[Range[nn],PrimeOmega[#]==2&]},Select[Range[ Length[sp]], Total[ IntegerDigits[sp[[#]]]] ==Total[ IntegerDigits[#]]&]] (* Harvey P. Dale, Oct 15 2012 *)

Formula

A007953(A001358(a(n))) = A007953(a(n)).

Extensions

Corrected and extended by Stefan Steinerberger and Robert G. Wilson v, Dec 29 2007