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a(n) is the least number whose product of digits in primorial base equals n.
1

%I #10 Jun 18 2022 08:41:42

%S 0,1,5,21,17,159,23,1509,29,111,161,25659,83,392949,1511,171,89,

%T 8711259,113,184837209,167,1521,25661,5141378799,119,1209,392951,741,

%U 1517,187854439329,173,6224078222919,149,25671,8711261,1629,203,274774574506989,184837211

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

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

%C Each prime number sets a new record.

%H Rémy Sigrist, <a href="/A355036/b355036.txt">Table of n, a(n) for n = 0..2356</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F A355037(a(n)) = n.

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

%e The first terms, alongside their primorial base expansion, are:

%e n a(n) pr(a(n))

%e -- --------- ------------------

%e 0 0 0

%e 1 1 1

%e 2 5 2_1

%e 3 21 3_1_1

%e 4 17 2_2_1

%e 5 159 5_1_1_1

%e 6 23 3_2_1

%e 7 1509 7_1_1_1_1

%e 8 29 4_2_1

%e 9 111 3_3_1_1

%e 10 161 5_1_2_1

%e 11 25659 11_1_1_1_1_1

%e 12 83 2_3_2_1

%e 13 392949 13_1_1_1_1_1_1

%o (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))) }

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

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, Jun 16 2022