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A225048
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Numbers that cannot be expressed as n plus the sum of the squared digits of n for any integer n.
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2
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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
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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26 is not in the sequence, because 21+2^2+1^2=26. However, no such solution exists for 25 or 27.
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MATHEMATICA
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nn=122; Complement[Range[nn], Table[n+Total[IntegerDigits[n]^2], {n, nn}]] (* Jayanta Basu, May 05 2013 *)
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PROG
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(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)))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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