A355036 a(n) is the least number whose product of digits in primorial base equals n.

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

Author

Rémy Sigrist, Jun 16 2022

Keywords

• nonn
• base

Comments

All terms except a(0) = 0 are odd.

Each prime number sets a new record.

Examples

			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
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..2356
• Index entries for sequences related to primorial base

Crossrefs

Cf. A005867, A057588, A263130 (factorial base analog), A355037.

Programs

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))) }

Formula

A355037(a(n)) = n.

a(A005867(n)) = A057588(n) for any n > 0.