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

Offset: 0

Author

Antti Karttunen, Jun 18 2024

Keywords

• sign
• base
• easy

Comments

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

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16170
• Index entries for sequences related to primorial base

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.

Programs

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); };

Formula

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

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