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

0,3

Comments

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

Each prime number sets a new record.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..2356

Index entries for sequences related to primorial base

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

Adjacent sequences: A355033 A355034 A355035 * A355037 A355038 A355039

Keyword

nonn,base

Author

Rémy Sigrist, Jun 16 2022

Status

approved