A328842 - OEIS

%I #9 Nov 01 2019 18:40:01

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A328842/b328842.txt">Table of n, a(n) for n = 0..30030</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

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

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

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

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

%o (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); };

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

%Y Cf. A276156 (positions of zeros).

%Y Cf. A276009 for analogous sequence.

%K nonn,base

%O 0,5

%A _Antti Karttunen_, Oct 30 2019