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A331565
The base 10 numbers with a digit product > 0 and which when written in bases 3,4,5,6,7,8,9 have two or more other base representations with the same digit product.
3
1, 2, 3, 4, 5, 6, 7, 91, 491, 921, 1138, 1234, 4853, 13581, 23568, 29242, 42161, 42162, 42163, 42164, 42991, 43365, 44313, 83342, 83651, 85226, 114382, 153881, 155462, 159422, 232868, 291862, 296183, 352486, 372642, 398543, 419563, 441194, 465326, 616146, 625431, 625523, 635813
OFFSET
1,2
COMMENTS
For terms 10 < a(n) < 10^9 none have a base-3 representation whose digit product equals the base-10 product. The first such entry using the base-4 representation is 491.
EXAMPLE
6 is a term as 6_10 = 6_7 = 6_8 = 6_9, so it has three other base representations where the digit product also equals 6.
91 is a term as 91_10 = 331_5 = 133_8, so it has two other base representations where the digit product also equals 9.
491 is a term as 491_10 = 13223_4 = 3431_5, so it has two other base representations where the digit product also equals 36.
MATHEMATICA
proDig[n_, b_] := Times @@ IntegerDigits[n, b]; seqQ[n_] := Module[{prod = proDig[n, 10], count = 0}, If[prod > 0, Do[If[proDig[n, b] == prod, count++]; If[count == 2, Break[]], {b, 3, 9}]]; count == 2]; Select[Range[650000], seqQ] (* Amiram Eldar, Jan 21 2020 *)
PROG
(PARI) isok(n) = {my(p=vecprod(digits(n))); (p != 0) && (sum(k=3, 9, p==vecprod(digits(n, k))) >= 2); } \\ Michel Marcus, Jan 21 2020
CROSSREFS
Subsequence of A052382 (zeroless numbers).
Sequence in context: A024649 A037335 A028429 * A171644 A246338 A037334
KEYWORD
nonn,base
AUTHOR
Scott R. Shannon, Jan 20 2020
STATUS
approved