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

0,4

Links

Antti Karttunen, Table of n, a(n) for n = 0..30030

Index entries for sequences related to primorial base.

Formula

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

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

Example

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.

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 *)

Prog

(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); };

Crossrefs

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

Cf. also A003132.

Sequence in context: A258066 A036501 A225153 * A308319 A167380 A242613

Adjacent sequences: A360105 A360106 A360107 * A360109 A360110 A360111

Keyword

nonn,base,easy,look

Author

Antti Karttunen, Jan 28 2023

Status

approved