A224792 Smallest skinny number (A061909) with digit sum n.

0, 1, 2, 3, 13, 113, 1113, 11113, 1011113, 101011113, 1101111211, 110101111211, 100110101111211, 10101010101101122, 1011111111100000013, 1010111111111000000022, 111000010111000111111111, 1010110111101110100000011111, 1111111110010101100001100000102

Offset: 0

Author

Reiner Moewald, Apr 18 2013

Keywords

• nonn
• base

Comments

The smallest m >= 0 with sum of digits of (m) = n and sum of digits of (m^2) = (sum of digits of (m))^2.

There are infinitely many natural numbers m >= 0 with sum of digits of (m) = n and sum of digits of (m^2) = (sum of digits of (m))^2.

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 0..19

Crossrefs

Cf. A061909.

Programs

Mathematica

DS[n_] := Total[IntegerDigits[n]]; nn = 10; t = Table[0, {nn}]; n = 0; found = 0; While[n++; r = FromDigits[IntegerDigits[n, 4]]; found < nn, If[DS[r]^2 == DS[r^2] && DS[r] <= nn && t[[DS[r]]] == 0, t[[DS[r]]] = r;  found++; Print[r]]]; Join[{0}, t] (* T. D. Noe, Apr 18 2013 *)

Formula

a(n) > 2/9 * 10^(n/2) for n > 4. - Charles R Greathouse IV, Apr 18 2013

Extensions

a(10) corrected and a(11) added by T. D. Noe, Apr 18 2013

a(12)-a(13) from Donovan Johnson, Apr 19 2013

a(14) from Donovan Johnson, Apr 24 2013

a(15)-a(18) from Hiroaki Yamanouchi, Aug 28 2014