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

Author

Farideh Firoozbakht, Dec 24 2004

Keywords

• base
• nonn

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).

Examples

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

Crossrefs

Cf. A014080, A049529, A101697.

Programs

Mathematica

Do[h = IntegerDigits[n]; l = Length[h]; If[FromDigits[Reverse[IntegerDigits[n]]] == Sum[h[[k]]!, {k, l}], Print[n]], {n, 10^9}]

Extensions

More terms from Donovan Johnson, Feb 26 2008