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

1,2

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.

Links

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000

Index entries for Colombian or self numbers and related sequences

Example

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

Mathematica

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

Prog

(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)))

Crossrefs

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

Sequence in context: A241687 A169757 A051374 * A357129 A116590 A024355

Adjacent sequences: A225045 A225046 A225047 * A225049 A225050 A225051

Keyword

nonn,base

Author

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

Status

approved