A119461 Zero-free numbers with digit sum equal to 7.

7, 16, 25, 34, 43, 52, 61, 115, 124, 133, 142, 151, 214, 223, 232, 241, 313, 322, 331, 412, 421, 511, 1114, 1123, 1132, 1141, 1213, 1222, 1231, 1312, 1321, 1411, 2113, 2122, 2131, 2212, 2221, 2311, 3112, 3121, 3211, 4111, 11113, 11122, 11131, 11212, 11221, 11311, 12112, 12121, 12211, 13111, 21112, 21121, 21211, 22111, 31111, 111112, 111121, 111211, 112111, 121111, 211111, 1111111

Offset: 1

Author

Zak Seidov, May 20 2006

Keywords

• base
• fini
• full
• nonn

Comments

There are exactly 64 such numbers while numbers with digit sum equal to 7 (A052221) are infinite.

Crossrefs

Subsequence of A052221.

Programs

Mathematica

Union[Flatten[Table[FromDigits/@Select[Tuples[Range[7],n],Total[#]==7&],{n,7}]]] (* Harvey P. Dale, Aug 29 2015 *)

Python

def ok(n): s = str(n); return '0' not in s and sum(map(int, s)) == 7
print(list(filter(ok, range(1111112)))) # Michael S. Branicky, Jul 16 2021