A225048 Numbers that cannot be expressed as n plus the sum of the squared digits of n for any integer n.

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, 40, 43, 46, 47, 48, 49, 50, 52, 55, 57, 60, 61, 63, 64, 65, 70, 71, 73, 74, 78, 79, 82, 84, 85, 88, 89, 91, 92, 93, 94, 97, 99, 100, 104, 106, 109, 110, 115, 120, 122

Offset: 1

Author

Kevin L. Schwartz and Christian N. K. Anderson, Apr 25 2013

Keywords

• nonn
• base

Comments

A natural extension of the Self or Colombian numbers (A003052).

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.

Examples

			26 is not in the sequence, because 21+2^2+1^2=26. However, no such solution exists for 25 or 27.
		

Links

• Christian N. K. Anderson, Table of n, a(n) for n = 1..10000
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Cf. A003052, A003219, A003132, A062028, A066568.

Programs

Mathematica

nn=122;Complement[Range[nn],Table[n+Total[IntegerDigits[n]^2],{n,nn}]] (* Jayanta Basu, May 05 2013 *)

R

digsqsum<-function(x) sum(as.numeric(unlist(strsplit(as.character(x),split="")))^2)
which(is.na(match(1:1000,1:1000+sapply(1:1000,digsqsum)))