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A241175
Numbers which cannot be obtained by adding some digit of a number m to m.
13
1, 3, 5, 7, 9, 21, 43, 65, 87
OFFSET
1,2
COMMENTS
Presumably there are no further terms.
Proof: We can check explicitly that there is no further term below 1000. Any larger number is of the form n = a*1000 + b, a > 0, with either 0 <= b < 100 (in which case n has a digit '0' and n = n + 0 is not in the sequence) or 87 < b < 1000 in which case b is not in this sequence, thus b = m+d where d is a digit of m and therefore also of a*1000 + m and therefore n = (a*1000 + m) + d is not in this sequence. - M. F. Hasler, Apr 26 2014
REFERENCES
Eric Angelini, Posting to Sequence Fans Mailing List, Apr 20 2014
EXAMPLE
Since 23 = 21+2, 23 is not on this list.
Numbers having a digit '0' can be written as n+0 and are excluded.
Numbers ending in digits d = 2, 4, 6 or 8 can be written as sum of m = n - d/2 and the trailing digit of m, d/2.
MATHEMATICA
l = 100; lst = Range[l];
Do[lst = Complement[lst, IntegerDigits[i] + i], {i, 1, l}];
lst (* Robert Price, Mar 20 2019 *)
PROG
(PARI) is(n)=n&&!for(i=0, min(n, 9), setsearch(Set(digits(n-i)), i)&&return) \\ M. F. Hasler, Apr 26 2014
CROSSREFS
KEYWORD
nonn,base,fini,full
AUTHOR
N. J. A. Sloane, Apr 23 2014
STATUS
approved