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A355036
a(n) is the least number whose product of digits in primorial base equals n.
1
0, 1, 5, 21, 17, 159, 23, 1509, 29, 111, 161, 25659, 83, 392949, 1511, 171, 89, 8711259, 113, 184837209, 167, 1521, 25661, 5141378799, 119, 1209, 392951, 741, 1517, 187854439329, 173, 6224078222919, 149, 25671, 8711261, 1629, 203, 274774574506989, 184837211
OFFSET
0,3
COMMENTS
All terms except a(0) = 0 are odd.
Each prime number sets a new record.
FORMULA
A355037(a(n)) = n.
a(A005867(n)) = A057588(n) for any n > 0.
EXAMPLE
The first terms, alongside their primorial base expansion, are:
n a(n) pr(a(n))
-- --------- ------------------
0 0 0
1 1 1
2 5 2_1
3 21 3_1_1
4 17 2_2_1
5 159 5_1_1_1
6 23 3_2_1
7 1509 7_1_1_1_1
8 29 4_2_1
9 111 3_3_1_1
10 161 5_1_2_1
11 25659 11_1_1_1_1_1
12 83 2_3_2_1
13 392949 13_1_1_1_1_1_1
PROG
(PARI) a(n) = { if (n==0, 0, my (v=0, f=1); forprime (r=2, oo, forstep (d=r-1, 1, -1, if (n%d==0, v+=f*d; n/=d; break; ); ); if (n==1, return (v), f*=r))) }
CROSSREFS
Cf. A005867, A057588, A263130 (factorial base analog), A355037.
Sequence in context: A346035 A167202 A204914 * A263130 A165204 A043053
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jun 16 2022
STATUS
approved