A185400 Numbers with property that the digital sum plus the product of the digits is a power of 2.

1, 2, 4, 8, 10, 20, 22, 40, 80, 100, 101, 103, 107, 110, 111, 113, 117, 130, 131, 133, 137, 170, 171, 173, 177, 200, 202, 206, 220, 260, 301, 305, 310, 311, 313, 317, 331, 350, 371, 400, 404, 440, 503, 530, 602, 620, 701, 709, 710, 711, 713, 717, 731, 771, 790, 800, 808, 880, 907, 970, 1000, 1001, 1003, 1007, 1010, 1012, 1016

Offset

1,2

Links

Table of n, a(n) for n=1..67.

Example

371 is in the sequence because (3+7+1) + (3*7*1) = 11 + 21 = 32 = 2^5.
116291 is in the sequence because (1+1+6+2+9+1) + (1*1*6*2*9*1) = 20 + 108 = 128 = 2^7.

Maple

A007953 := proc(n) add(d, d=convert(n, base, 10)) ; end proc:
A007954 := proc(n) mul(d, d=convert(n, base, 10)) ; end proc:
A061762 := proc(n) A007953(n)+A007954(n) ; end proc:
isA000079 := proc(n) if n < 1 then false; elif n = 1 then true; else if type(n, 'even') then is( nops(numtheory[factorset](n)) = 1) ; else false; end if; end if; end proc:
isA185400 := proc(n) isA000079(A061762(n)) ; end proc:
for n from 1 to 1300 do if isA185400(n) then printf("%a, ", n) ; end if; end do: # R. J. Mathar, Feb 08 2011

Mathematica

pwrs2Q[n_]:=Module[{idn=IntegerDigits[n], x, y}, x=Total[idn]+Times@@idn; y=Round[Log[x]/Log[2]]; 2^y==x]
Select[Range[1100], pwrs2Q]  (* Harvey P. Dale, Feb 16 2011 *)

Crossrefs

Cf A061762.

Sequence in context: A173816 A287266 A306719 * A099942 A033092 A177909

Adjacent sequences: A185397 A185398 A185399 * A185401 A185402 A185403

Keyword

nonn,base

Author

Michel Lagneau, Feb 03 2011

Status

approved