A351567 - OEIS

%I #13 Mar 13 2024 01:51:06

%S 0,0,0,1,0,2,0,1,1,1,1,2,0,2,2,1,2,2,0,3,3,1,3,2,0,4,4,1,4,2,0,1,1,1,

%T 1,2,1,1,1,1,1,2,1,2,2,1,2,2,1,3,3,1,3,2,1,4,4,1,4,2,0,2,2,1,2,2,2,1,

%U 1,1,1,2,2,2,2,1,2,2,2,3,3,1,3,2,2,4,4,1,4,2,0,3,3,1,3,2,3,1,1,1,1,2,3,2,2,1

%N The second least significant nonzero digit in the primorial base expansion of n, or 0 if there is no such digit.

%H Antti Karttunen, <a href="/A351567/b351567.txt">Table of n, a(n) for n = 0..60060</a>

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

%F a(n) = A351563(A276086(n)).

%F For all n, a(n) < A351566(n).

%t a[n_] := Module[{k = n, p = 2, s = {}, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, If[r > 0, AppendTo[s, r]]; p = NextPrime[p]]; i = Position[s, _?(# > 0 &)] // Flatten; If[Length[s] < 2, 0, s[[2]]]]; Array[a, 100, 0] (* _Amiram Eldar_, Mar 13 2024 *)

%o (PARI)

%o A351563(n) = if(1>=omega(n), 0, (factor(n))[2,2]);

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A351567(n) = A351563(A276086(n));

%Y Cf. A060735 (gives the positions of zeros after a(0)=0).

%Y Cf. A049345, A276086, A351563, A351566.

%K nonn,base

%O 0,6

%A _Antti Karttunen_, Apr 01 2022