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A131418 Numbers n such that Sum_digits(n)=Sum_digits[n+Sum_digits(n)], with n>=0. 2

%I

%S 0,9,18,27,36,45,54,63,72,81,108,117,126,135,144,153,162,171,207,216,

%T 225,234,243,252,261,279,306,315,324,333,342,351,369,378,405,414,423,

%U 432,441,459,468,477,504,513,522,531,549,558,567,576,603,612,621,639

%N Numbers n such that Sum_digits(n)=Sum_digits[n+Sum_digits(n)], with n>=0.

%C Conjecture: all terms are divisible by 9. - _Harvey P. Dale_, Mar 28 2019

%e n=315 --> 3+1+5=9 --> 315+9=324 --> 3+2+4=9.

%e n=873 --> 8+7+3=18 --> 873+18=891 --> 8+9+1=18.

%p P:=proc(n) local a,i,k,w; 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; a:=w; k:=i+w; w:=0; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if a=w then print(i); fi; od; end: P(1000);

%t Select[Range[0,700],Total[IntegerDigits[#]]==Total[IntegerDigits[#+ Total[ IntegerDigits[ #]]]]&] (* _Harvey P. Dale_, Mar 28 2019 *)

%o (PARI) isok(n) = my(sn = sumdigits(n)); sn == sumdigits(n+sn); \\ _Michel Marcus_, May 10 2019

%Y Cf. A007953, A131417.

%K easy,nonn,base

%O 1,2

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Jul 09 2007

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Last modified September 26 21:46 EDT 2020. Contains 337377 sequences. (Running on oeis4.)