A360108 Sum of squares of digits of primorial base expansion of n.

0, 1, 1, 2, 4, 5, 1, 2, 2, 3, 5, 6, 4, 5, 5, 6, 8, 9, 9, 10, 10, 11, 13, 14, 16, 17, 17, 18, 20, 21, 1, 2, 2, 3, 5, 6, 2, 3, 3, 4, 6, 7, 5, 6, 6, 7, 9, 10, 10, 11, 11, 12, 14, 15, 17, 18, 18, 19, 21, 22, 4, 5, 5, 6, 8, 9, 5, 6, 6, 7, 9, 10, 8, 9, 9, 10, 12, 13, 13, 14, 14, 15, 17, 18, 20, 21, 21, 22

Offset: 0

Author

Antti Karttunen, Jan 28 2023

Keywords

• nonn
• base
• easy
• look

Examples

			5 in primorial base (A049345) is written as "21" (because 5 = 2*2 + 1*1), therefore a(5) = 2^2 + 1^2 = 5.
23 in primorial base is written as "321" (because 23 = 3*6 + 2*2 + 1*1), therefore a(23) = 3^2 + 2^2 + 1^2 = 14.
24 in primorial base is written as "400" (because 24 = 4*6 + 0*2 + 0*1), therefore a(24) = 4^2 = 16.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..30030
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A002110 (positions of 1's), A049345, A090885, A276086, A276150.

Cf. also A003132.

Programs

Mathematica

a[n_] := Module[{k = n, p = 2, s = 0, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, s += r^2; p = NextPrime[p]]; s]; Array[a, 100, 0] (* Amiram Eldar, Mar 06 2024 *)

PARI

A360108(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d^2; n = (n-d)/p; p = nextprime(1+p)); (s); };

Formula

a(n) = A090885(A276086(n)).

For all n >= 0, a(2n+1) = 1 + a(2n).