A241175 Numbers which cannot be obtained by adding some digit of a number m to m.

1, 3, 5, 7, 9, 21, 43, 65, 87

Offset: 1

Author

N. J. A. Sloane, Apr 23 2014

Keywords

• nonn
• base
• fini
• full

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

Examples

			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.
		

References

• Eric Angelini, Posting to Sequence Fans Mailing List, Apr 20 2014

Crossrefs

Related sequences: A241173, A241174, A241175, A241176, A241177, A241178, A241179, A241180, A241181, A241182, A241183.

Programs

Mathematica

l = 100; lst = Range[l];
Do[lst = Complement[lst, IntegerDigits[i] + i], {i, 1, l}];
lst (* Robert Price, Mar 20 2019 *)

PARI

is(n)=n&&!for(i=0,min(n,9),setsearch(Set(digits(n-i)),i)&&return) \\ M. F. Hasler, Apr 26 2014