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A329348
The least significant nonzero digit in the primorial base expansion of primorial inflation of n, A108951(n).
14
1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 6, 2, 1, 2, 1, 4, 6, 2, 1, 3, 2, 2, 1, 4, 1, 5, 1, 1, 6, 2, 8, 4, 1, 2, 6, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 4, 6, 4, 1, 2, 4, 8, 6, 2, 1, 3, 1, 2, 3, 2, 13, 12, 1, 4, 6, 5, 1, 3, 1, 2, 5, 4, 2, 12, 1, 2, 1, 2, 1, 2, 11, 2, 6, 8, 1, 2, 6, 4, 6, 2, 7, 2, 1, 2, 10, 1, 1, 12, 1, 8, 4
OFFSET
1,4
COMMENTS
Number of occurrences of the least primorial present in the greedy sum of primorials adding to A108951(n).
The greedy sum is also the sum with the minimal number of primorials, used for example in the primorial base representation.
FORMULA
a(n) = A067029(A324886(n)) = A276088(A108951(n)).
a(n) <= A324888(n).
From Antti Karttunen, Jan 15-17 2020: (Start)
a(n) = A331188(n) mod A117366(n).
a(n) = A001511(A246277(A324886(n))).
(End)
EXAMPLE
For n = 24 = 2^3 * 3, A108951(24) = A034386(2)^3 * A034386(3) = 2^3 * 6 = 48 = 1*30 + 3*6, and as the factor of the least primorial in the sum is 3, we have a(24) = 3.
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
A276088(n) = { my(e=0, p=2); while(n && !(e=(n%p)), n = n/p; p = nextprime(1+p)); (e); };
(PARI)
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A067029(n) = if(1==n, 0, factor(n)[1, 2]); \\ From A067029
(PARI)
A002110(n) = prod(i=1, n, prime(i));
A329348(n) = if(1==n, n, my(f=factor(n), p=nextprime(1+vecmax(f[, 1]))); prod(i=1, #f~, A002110(primepi(f[i, 1]))^(f[i, 2]-(#f~==i)))%p); \\ Antti Karttunen, Jan 15 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 11 2019
EXTENSIONS
Name changed by Antti Karttunen, Jan 17 2020
STATUS
approved