%I #24 Nov 01 2013 17:11:38
%S 1,3,4,5,7,8,9,10,14,15,16,18,19,21,22,25,27,28,29,32,33,34,35,37,38,
%T 40,43,46,47,48,49,50,52,55,57,60,61,63,64,65,70,71,73,74,78,79,82,84,
%U 85,88,89,91,92,93,94,97,99,100,104,106,109,110,115,120,122
%N Numbers that cannot be expressed as n plus the sum of the squared digits of n for any integer n.
%C A natural extension of the Self or Colombian numbers (A003052).
%C Up to 144, there are more numbers that cannot be expressed in this way than numbers that can. Thereafter, there are always more numbers that can.
%H Christian N. K. Anderson, <a href="/A225048/b225048.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%e 26 is not in the sequence, because 21+2^2+1^2=26. However, no such solution exists for 25 or 27.
%t nn=122;Complement[Range[nn],Table[n+Total[IntegerDigits[n]^2],{n,nn}]] (* _Jayanta Basu_, May 05 2013 *)
%o (R) digsqsum<-function(x) sum(as.numeric(unlist(strsplit(as.character(x),split="")))^2)
%o which(is.na(match(1:1000,1:1000+sapply(1:1000,digsqsum)))
%Y Cf. A003052, A003219, A003132, A062028, A066568.
%K nonn,base
%O 1,2
%A _Kevin L. Schwartz_ and _Christian N. K. Anderson_, Apr 25 2013