cp's OEIS Frontend

A329343 Difference between the indices of the smallest and the largest primorial in the greedy sum of primorials adding to A108951(n).

%I A329343 #9 Nov 11 2019 18:43:31
%S A329343 0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,1,0,0,0,0,0,1,1,0,2,0,0,1,0,2,0,0,
%T A329343 1,1,0,0,0,1,0,1,0,0,1,0,0,1,2,1,0,0,0,2,1,0,0,0,0,1,0,0,1,2,1,0,0,0,
%U A329343 0,1,0,2,0,0,2,0,1,0,0,1,2,0,0,1,1,0,0,0,0,1,1,0,0,0,1,1,0,2,1,2,0,0,0,0,2
%N A329343 Difference between the indices of the smallest and the largest primorial in the greedy sum of primorials adding to A108951(n).
%C A329343 The greedy sum is also the sum with the minimal number of primorials, used for example in the primorial base representation.
%C A329343 Positions of the records (and conjecturally, the positions of the first occurrences of each n) begin as 1, 8, 27, 162, 289, 529, 841, 1369, 1681, 2209, 2809, 3481, 4489, 5041, 5329, 6889, ..., that after 162 all seem to be squares of certain primes. See also A329051.
%H A329343 Antti Karttunen, <a href="/A329343/b329343.txt">Table of n, a(n) for n = 1..65537</a>
%H A329343 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A329343 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A329343 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A329343 a(n) = A243055(A324886(n)).
%e A329343 For n = 18 = 2 * 3^2, A108951(18) = A034386(2) * A034386(3)^2 = 2 * 6^2 = 72 = 30 + 30 + 6 + 6, and as the largest primorial in the sum is 30 = A002110(3), and the least primorial is 6 = A002110(2), we have a(18) = 3-2 = 1.
%o A329343 (PARI)
%o A329343 A034386(n) = prod(i=1, primepi(n), prime(i));
%o A329343 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
%o A329343 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A329343 A324886(n) = A276086(A108951(n));
%o A329343 A243055(n) = if(1==n,0,my(f = factor(n), lpf = f[1, 1], gpf = f[#f~, 1]); (primepi(gpf)-primepi(lpf)));
%o A329343 A329343(n) = A243055(A324886(n));
%Y A329343 Cf. A002110, A034386, A108951, A243055, A276086, A324886, A324888, A329040, A329051.
%K A329343 nonn
%O A329343 1,27
%A A329343 _Antti Karttunen_, Nov 11 2019