A045670 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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