A101702 Numbers m such that the sum of the factorials of their digits is equal to the reversal of m.

1, 2, 541, 52100, 58504, 66410, 430000, 863180, 8601400, 17927300, 27927300, 31000000, 665100000, 3715000000, 6739630000, 11000000000, 21000000000, 53100000000, 70858000000, 79637300000, 451000000000, 1715000000000, 2715000000000, 48304000000000, 340000000000000, 5520000000000000

Offset

1,2

Comments

If s=sum of the factorials of digits of m & reversal(m) >= s then 10^(reversal(m) - s)*m is in the sequence. Example m=23; s = 2! + 3!; reversal(23) - s = 24 & 23*10^24 is in the sequence. So this sequence is infinite because there exist infinitely many numbers m such that reversal(m) > s. If m is a k-digit term of this sequence and the first digit of m is 1 then 10^(k-1) + m is also in the sequence. Examples: m=1 so 10^(1-1) + 1 = 2 is in the sequence, m=17927300 so 10^7 + 17927300 = 27927300 is in the sequence. If m > 5 then 10 divides a(m). If 10 doesn't divide a(m) then the reversal of m is in the sequence A014080, so all terms of A014080 are: reversal(1), reversal(2), reversal(541) & reversal(58504).

Links

Table of n, a(n) for n=1..26.

Example

665100000 is in the sequence because reversal(665100000) = 1566 = 6! + 6! + 5! + 1! + 0! + 0! + 0! + 0! + 0!.

Mathematica

Do[h = FactorInteger[n]; l = Length[h]; If[FromDigits[Reverse[IntegerDigits[n] == Sum[h[[k]]], {k, l}], Print[n]], {n, 800000000}]

Crossrefs

Cf. A014080, A049529, A101697.

Sequence in context: A262649 A202277 A177836 * A119780 A120840 A348174

Adjacent sequences: A101699 A101700 A101701 * A101703 A101704 A101705

Keyword

base,nonn

Author

Farideh Firoozbakht, Dec 24 2004

Extensions

More terms from Donovan Johnson, Feb 26 2008

Status

approved