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A282782 Numbers n that are equal to a product of powers of digits where the exponents from left to right decrease with 1 and the exponent for the units digit is 1. 0
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1715 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Up to 10^9 no other number matches the rule.

There are no other terms up to 10^200; this list is probably complete. - Charles R Greathouse IV, Feb 22 2017

LINKS

Table of n, a(n) for n=1..11.

EXAMPLE

1 = 1^1, 2 = 2^1, ..., 1715 = (1^4)*(7^3)*(1^2)*(5^1).

These numbers do not match the rule:

46: (4^2)*(6^1) = 96 <> 46.

234: (2^3)*(3^2)*(4^1) = 288 <> 234.

4342: (4^4)*(3^3)*(4^2)*(2^1) = 221184 <> 4342.

46914: (4^5)*(6^4)*(9^3)*(1^2)*(4^1) = 3869835264 <> 46914.

MATHEMATICA

mx = 10^50; test[n_] := n == Times @@ (IntegerDigits[n] ^Reverse[Range@ IntegerLength@ n]); Union@Reap[Do[n = 2^i 3^j 7^k; If[test@n, Sow@n], {i, 0, Log2[mx]}, {j, 0, Log[3, mx/2^i]}, {k, 0, Log[7, mx/2^i/3^j]}]; Do[n = 5  3^j 7^k; If[test@n, Sow@n], {j, 0, Log[3, mx/5]}, {k, 0, Log[7, mx/ 5/ 3^j]}]][[2, 1]] (* Search up to 10^50, Giovanni Resta, Feb 22 2017 *)

Select[Range[0, 2000], Times @@ MapIndexed[#1^First[#2] &, Reverse@ IntegerDigits@ #] == # &] (* Michael De Vlieger, Feb 22 2017 *)

PROG

(VBA) ' For example for 5-figure numbers:

Dim zahl As String

For i = 10000 To 99999

zahl = i

If i = CInt(Left(zahl, 1)) ^ 5 * CInt(Right(Left(zahl, 2), 1)) ^ 4 * CInt(Right(Left(zahl, 3), 1)) ^ 3 * CInt(Right(Left(zahl, 4), 1)) ^ 2 * CInt(Right(zahl, 1)) ^ 1 Then

MsgBox (i)

End If

Next i

(PARI) is(n)=my(d=digits(n)); prod(i=1, #d, d[#d+1-i]^i)==n || !n \\ Charles R Greathouse IV, Feb 22 2017

(PARI) list(lim)=my(v=List([0]), t7, t37, t); for(a=0, logint(lim\1, 7), t7=7^a; for(b=0, logint(lim\t7, 3), t=t37=t7*3^b; while(t<=lim, if(is(t), listput(v, t)); t<<=1); t=t37; while(t<=lim, if(is(t), listput(v, t)); t*=5))); Set(v) \\ Charles R Greathouse IV, Feb 22 2017

CROSSREFS

Subsequence of A002473; apart from the first term, a subsequence of A238985.

Sequence in context: A223081 A077727 A032557 * A032565 A004915 A135385

Adjacent sequences:  A282779 A282780 A282781 * A282783 A282784 A282785

KEYWORD

nonn,base

AUTHOR

Shmelev Aleksei, Feb 21 2017

EXTENSIONS

Leading 0 prepended by David A. Corneth, Feb 22 2017

STATUS

approved

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Last modified October 23 18:46 EDT 2018. Contains 316530 sequences. (Running on oeis4.)