A328842 Decrement each nonzero digit by one in primorial base representation of n, then convert back to decimal.

0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 6, 6, 6, 6, 8, 8, 12, 12, 12, 12, 14, 14, 18, 18, 18, 18, 20, 20, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 6, 6, 6, 6, 8, 8, 12, 12, 12, 12, 14, 14, 18, 18, 18, 18, 20, 20, 30, 30, 30, 30, 32, 32, 30, 30, 30, 30, 32, 32, 36, 36, 36, 36, 38, 38, 42, 42, 42, 42, 44, 44, 48, 48, 48, 48, 50, 50, 60, 60

Offset: 0

Author

Antti Karttunen, Oct 30 2019

Keywords

• nonn
• base

Links

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

Crossrefs

Cf. A002110, A003557, A276085, A276086, A328114, A328572, A328841, A328844.

Cf. A276156 (positions of zeros).

Cf. A276009 for analogous sequence.

Programs

PARI

A328842(n) = { my(p=2, r=1, s=0); while(n, if((n%p)>0, s += ((n%p)-1)*r); r *= p; n = n\p; p = nextprime(1+p)); (s); };

Formula

a(n) = n - A328841(n).

a(n) = A276085(A328572(n)) = A276085(A003557(A276086(n))).

For all n >= 0, a(A276086(n)) = A328844(n).

For all n >= 1, A328114(a(n)) = A328114(n) - 1.