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

Author

Michel Lagneau, Feb 03 2011

Keywords

• nonn
• base

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A061762.

Programs

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 *)