A135210 Numbers n such that Sum_digits(n) + Sum_digits(n+1) = Sum_digits(2*n+1).

0, 1, 2, 3, 4, 9, 10, 11, 12, 13, 14, 19, 20, 21, 22, 23, 24, 29, 30, 31, 32, 33, 34, 39, 40, 41, 42, 43, 44, 49, 99, 100, 101, 102, 103, 104, 109, 110, 111, 112, 113, 114, 119, 120, 121, 122, 123, 124, 129, 130, 131, 132, 133, 134, 139, 140, 141, 142, 143, 144, 149

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Dec 18 2007

Keywords

• easy
• nonn
• base

Examples

			n=19 -> Sum_digits(19)=10; Sum_digits(20)=2 -> 10+2=12; Sum_digits(19+20)=12
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A127273.

Programs

Maple

P:=proc(n) local a,b,i,k,w,y,x; for i from 0 by 1 to n do w:=0; k:=i; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; x:=0; k:=i+1; while k>0 do x:=x+k-(trunc(k/10)*10); k:=trunc(k/10); od; y:=0; k:=2*i+1; while k>0 do y:=y+k-(trunc(k/10)*10); k:=trunc(k/10); od; if w+x=y then print(i); fi; od; end: P(1000);

Mathematica

Select[Range[0,1000], Total[IntegerDigits[#]] + Total[IntegerDigits[# + 1]] == Total[IntegerDigits[ 2*# + 1]] &] (* G. C. Greubel, Oct 01 2016 *)

PARI

is(n)=my(s=sumdigits,t); t=s(2*n+1)-s(n); t>0 && t==s(n+1) \\ Charles R Greathouse IV, Oct 01 2016