A373605 - OEIS

A373605

Sum of the even-indexed digits minus the sum of the odd-indexed digits in the primorial base representation (A049345) of n.

0, 1, -1, 0, -2, -1, 1, 2, 0, 1, -1, 0, 2, 3, 1, 2, 0, 1, 3, 4, 2, 3, 1, 2, 4, 5, 3, 4, 2, 3, -1, 0, -2, -1, -3, -2, 0, 1, -1, 0, -2, -1, 1, 2, 0, 1, -1, 0, 2, 3, 1, 2, 0, 1, 3, 4, 2, 3, 1, 2, -2, -1, -3, -2, -4, -3, -1, 0, -2, -1, -3, -2, 0, 1, -1, 0, -2, -1, 1, 2, 0, 1, -1, 0, 2, 3, 1, 2, 0, 1, -3, -2, -4, -3, -5, -4, -2, -1, -3

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OFFSET

0,5

COMMENTS

Alternating digit sum in primorial base, starting with a positive sign for the rightmost (least significant) digit.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..16170

Index entries for sequences related to primorial base

FORMULA

a(n) = A373606(n) - A373607(n).

a(n) = A195017(A276086(n)).

EXAMPLE

A049345(85) = 2401, thus the sum of digits at even positions (with the rightmost digit having index 0) is 1+4 = 5, and at the odd positions 0+2 = 2, therefore a(85) = 5-2 = 3.

PROG

(PARI) A373605(n) = { my(p=2, i=1, s=0); while(n, s += i*(n%p); n = n\p; p = nextprime(1+p); i = -i); (s); };

CROSSREFS

Cf. A049345, A195017, A276086, A373606, A373607, A373830, A373831 (indices of multiples of 3).

Analogous sequences for bases 2-10: A065359, A065368, A346688, A346689, A346690, A346691, A346731, A346732, A055017.

Sequence in context: A099917 A137412 A355913 * A025925 A372510 A240857

Adjacent sequences: A373602 A373603 A373604 * A373606 A373607 A373608

KEYWORD

sign,base,easy

AUTHOR

Antti Karttunen, Jun 18 2024

STATUS

approved