

A225048


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


2



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
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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 * A116590 A024355 A194413
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



