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 A329343 Difference between the indices of the smallest and the largest primorial in the greedy sum of primorials adding to A108951(n). 8
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,27 COMMENTS The greedy sum is also the sum with the minimal number of primorials, used for example in the primorial base representation. 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. LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 FORMULA a(n) = A243055(A324886(n)). EXAMPLE 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. PROG (PARI) A034386(n) = prod(i=1, primepi(n), prime(i)); A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); }; A324886(n) = A276086(A108951(n)); A243055(n) = if(1==n, 0, my(f = factor(n), lpf = f[1, 1], gpf = f[#f~, 1]); (primepi(gpf)-primepi(lpf))); A329343(n) = A243055(A324886(n)); CROSSREFS Cf. A002110, A034386, A108951, A243055, A276086, A324886, A324888, A329040, A329051. Sequence in context: A321912 A329921 A092303 * A063725 A084888 A091400 Adjacent sequences:  A329340 A329341 A329342 * A329344 A329345 A329346 KEYWORD nonn AUTHOR Antti Karttunen, Nov 11 2019 STATUS approved

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Last modified September 17 16:45 EDT 2021. Contains 347487 sequences. (Running on oeis4.)