cp's OEIS Frontend

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

%I A241175 #15 Mar 21 2019 02:39:50
%S A241175 1,3,5,7,9,21,43,65,87
%N A241175 Numbers which cannot be obtained by adding some digit of a number m to m.
%C A241175 Presumably there are no further terms.
%C A241175 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
%D A241175 Eric Angelini, Posting to Sequence Fans Mailing List, Apr 20 2014
%e A241175 Since 23 = 21+2, 23 is not on this list.
%e A241175 Numbers having a digit '0' can be written as n+0 and are excluded.
%e A241175 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.
%t A241175 l = 100; lst = Range[l];
%t A241175 Do[lst = Complement[lst, IntegerDigits[i] + i], {i, 1, l}];
%t A241175 lst (* _Robert Price_, Mar 20 2019 *)
%o A241175 (PARI) is(n)=n&&!for(i=0,min(n,9),setsearch(Set(digits(n-i)),i)&&return) \\ _M. F. Hasler_, Apr 26 2014
%Y A241175 Related sequences: A241173, A241174, A241175, A241176, A241177, A241178, A241179, A241180, A241181, A241182, A241183.
%K A241175 nonn,base,fini,full
%O A241175 1,2
%A A241175 _N. J. A. Sloane_, Apr 23 2014