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A328615 Number of digits larger than 1 in primorial base expansion of n.

%I A328615 #14 Mar 13 2024 01:50:27
%S A328615 0,0,0,0,1,1,0,0,0,0,1,1,1,1,1,1,2,2,1,1,1,1,2,2,1,1,1,1,2,2,0,0,0,0,
%T A328615 1,1,0,0,0,0,1,1,1,1,1,1,2,2,1,1,1,1,2,2,1,1,1,1,2,2,1,1,1,1,2,2,1,1,
%U A328615 1,1,2,2,2,2,2,2,3,3,2,2,2,2,3,3,2,2,2,2,3,3,1,1,1,1,2,2,1,1,1,1,2,2,2,2,2,2
%N A328615 Number of digits larger than 1 in primorial base expansion of n.
%H A328615 Antti Karttunen, <a href="/A328615/b328615.txt">Table of n, a(n) for n = 0..32768</a>
%H A328615 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%F A328615 a(n) = A267263(n) - A328614(n).
%F A328615 a(n) = A001221(A328572(n)).
%e A328615 In primorial base (A049345), 87 is written as "2411" because 87 = 2*A002110(3) + 4*A002110(2) + 1*A002110(1) + 1*A002110(0) = 2*30 + 4*6 + 1*2 + 1*1. Only the digits 2 and 4 of these are larger than one, thus a(87) = 2.
%t A328615 a[n_] := Module[{k = n, p = 2, s = 0, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, If[r > 1, s++]; p = NextPrime[p]]; s]; Array[a, 100, 0] (* _Amiram Eldar_, Mar 13 2024 *)
%o A328615 (PARI) A328615(n) = { my(s=0, p=2); while(n, s += (1<(n%p)); n = n\p; p = nextprime(1+p)); (s); };
%Y A328615 Cf. A001221, A002110, A049345, A267263, A276086, A328114, A328572, A328614, A328616.
%K A328615 nonn,base
%O A328615 0,17
%A A328615 _Antti Karttunen_, Oct 22 2019