cp's OEIS Frontend

A351067 Number of integers between the n-th and the (n+1)-th primorial such that the maximal exponent in their prime factorization is larger than the maximal digit in their primorial base expansion.

%I A351067 #13 Feb 02 2022 15:09:15
%S A351067 0,3,11,52,291,1681,11506,89347
%N A351067 Number of integers between the n-th and the (n+1)-th primorial such that the maximal exponent in their prime factorization is larger than the maximal digit in their primorial base expansion.
%C A351067 a(n) is the number of terms of A350075 in range A002110(n) .. A002110(1+n)-1.
%C A351067 The ratio a(n) / A061720(n) develops as:
%C A351067 n = 1:     0 / 4           = 0
%C A351067     2:     3 / 24          = 0.125
%C A351067     3:    11 / 180         = 0.061111...
%C A351067     4:    52 / 2100        = 0.247619...
%C A351067     5:   291 / 27720       = 0.010498...
%C A351067     6:  1681 / 480480      = 0.003499...
%C A351067     7: 11506 / 9189180     = 0.001252...
%C A351067     8: 89347 / 213393180   = 0.000419...
%H A351067 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A351067 a(n) = Sum_{k=A002110(n) .. A002110(1+n)-1} [A328114(k) < A051903(k)], where [ ] is the Iverson bracket.
%F A351067 For all n, a(n) < A351069(n).
%e A351067 Between A002110(2) = 6 and A002110(3) = 30, there are exactly three numbers that satisfy the condition: 8, 9, 16, therefore a(2) = 3.
%o A351067 (PARI)
%o A351067 A002110(n) = prod(i=1,n,prime(i));
%o A351067 A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
%o A351067 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A351067 isA350075(n) = (A051903(A276086(n)) < A051903(n));
%o A351067 A351067(n) = sum(k=A002110(n),A002110(1+n)-1,isA350075(k));
%Y A351067 Cf. A002110, A051903, A276086, A328114, A350075, A351068 (partial sums), A351069.
%Y A351067 Cf. also A327969.
%K A351067 nonn,more
%O A351067 1,2
%A A351067 _Antti Karttunen_, Feb 02 2022