A045670 Digital sum (in base 10) of numbers in base 3 of the alternate number system.

1, 2, 3, 2, 3, 4, 3, 4, 5, 4, 5, 6, 3, 4, 5, 4, 5, 6, 5, 6, 7, 4, 5, 6, 5, 6, 7, 6, 7, 8, 5, 6, 7, 6, 7, 8, 7, 8, 9, 4, 5, 6, 5, 6, 7, 6, 7, 8, 5, 6, 7, 6, 7, 8, 7, 8, 9, 6, 7, 8, 7, 8, 9, 8, 9, 10, 5, 6, 7, 6, 7, 8, 7, 8, 9, 6, 7, 8, 7, 8, 9, 8, 9, 10, 7, 8, 9, 8, 9, 10

Offset: 1

Author

Bob Forslund (forslund(AT)tbaytel.net)

Keywords

• base
• nonn

Comments

The alternate number system has no need for the digit zero.

References

• Robert R. Forslund, A Logical Alternative to the Existing Positional Number System, Southwest Journal of Pure and Applied Mathematics. Vol. 1 1995 pp. 27-29.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..10000
• R. R. Forslund, A logical alternative to the existing positional number system, Southwest Journal of Pure and Applied Mathematics, 1995 Vol. 1.
• R. R. Forslund, Positive Integer Pages
• EMIS, Mirror site for Southwest Journal of Pure and Applied Mathematics

Crossrefs

Cf. A007931, A007932, A007953.

Programs

PARI

a(n)={my(k=3); while(n>k, n-=k; k*=3); my(d=digits(n+k-1,3)); vecsum(d) + #d - 2} \\ Andrew Howroyd, Jan 27 2020

Formula

a(n) = A007953(A007932(n)). - Andrew Howroyd, Jan 27 2020

Extensions

Terms a(25) and beyond from Andrew Howroyd, Jan 27 2020