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

1,2

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

Formula

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

Prog

(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

Crossrefs

Cf. A007931, A007932, A007953.

Sequence in context: A275868 A100795 A045781 * A363678 A194960 A111439

Adjacent sequences: A045667 A045668 A045669 * A045671 A045672 A045673

Keyword

base,nonn

Author

Bob Forslund (forslund(AT)tbaytel.net)

Extensions

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

Status

approved