A133608 - OEIS

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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

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OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..54.

FORMULA

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

EXAMPLE

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

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 *)

CROSSREFS

Cf. A001358, A007953, A033549.

Sequence in context: A163772 A056509 A129722 * A317444 A072577 A231182

Adjacent sequences: A133605 A133606 A133607 * A133609 A133610 A133611

KEYWORD

base,easy,nonn,less

AUTHOR

Jonathan Vos Post, Dec 27 2007

EXTENSIONS

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

STATUS

approved