A133608 - OEIS

%I #10 Sep 16 2015 13:46:49

%S 5,6,19,40,41,42,70,71,85,89,128,148,149,166,199,246,257,271,285,327,

%T 339,346,448,449,469,484,566,592,605,617,634,643,644,676,682,694,710,

%U 713,719,740,748,751,752,753,782,793,794,797,798,815,890,901,905,961

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

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

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

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

%t 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 *)

%t 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_ *)

%t nn=5000;With[{sp=Select[Range[nn],PrimeOmega[#]==2&]},Select[Range[ Length[sp]], Total[ IntegerDigits[sp[[#]]]] ==Total[ IntegerDigits[#]]&]] (* _Harvey P. Dale_, Oct 15 2012 *)

%Y Cf. A001358, A007953, A033549.

%K base,easy,nonn,less

%O 1,1

%A _Jonathan Vos Post_, Dec 27 2007

%E Corrected and extended by _Stefan Steinerberger_ and _Robert G. Wilson v_, Dec 29 2007