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.

0, 3, 11, 52, 291, 1681, 11506, 89347

Offset

1,2

Comments

a(n) is the number of terms of A350075 in range A002110(n) .. A002110(1+n)-1.

The ratio a(n) / A061720(n) develops as:

n = 1: 0 / 4 = 0

2: 3 / 24 = 0.125

3: 11 / 180 = 0.061111...

4: 52 / 2100 = 0.247619...

5: 291 / 27720 = 0.010498...

6: 1681 / 480480 = 0.003499...

7: 11506 / 9189180 = 0.001252...

8: 89347 / 213393180 = 0.000419...

Links

Table of n, a(n) for n=1..8.

Index entries for sequences related to primorial base

Formula

a(n) = Sum_{k=A002110(n) .. A002110(1+n)-1} [A328114(k) < A051903(k)], where [ ] is the Iverson bracket.

For all n, a(n) < A351069(n).

Example

Between A002110(2) = 6 and A002110(3) = 30, there are exactly three numbers that satisfy the condition: 8, 9, 16, therefore a(2) = 3.

Prog

(PARI)
A002110(n) = prod(i=1, n, prime(i));
A051903(n) = if((1==n), 0, vecmax(factor(n)[, 2]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
isA350075(n) = (A051903(A276086(n)) < A051903(n));
A351067(n) = sum(k=A002110(n), A002110(1+n)-1, isA350075(k));

Crossrefs

Cf. A002110, A051903, A276086, A328114, A350075, A351068 (partial sums), A351069.

Cf. also A327969.

Sequence in context: A367046 A179322 A014510 * A058799 A357833 A054362

Adjacent sequences: A351064 A351065 A351066 * A351068 A351069 A351070

Keyword

nonn,more

Author

Antti Karttunen, Feb 02 2022

Status

approved