A284672 Exponents of powers of 7 that contain all ten decimal digits.

18, 27, 34, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100

Offset: 1

Author

Seiichi Manyama, Apr 01 2017

Keywords

• nonn

Comments

It is conjectured that a(n) = n + 34 for n > 27.

Examples

			7^18 = 1628413597910449, which contains three 1's, one 2, one 3, three 4's, one 5, one 6, one 7, one 8, three 9's and one 0, so 18 is in the sequence.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A130694 (k=2), A236673 (k=3), A284670 (k=5), this sequence (k=7).

Formula

G.f.: x*(-x^28 + x^27 - x^7 + x^6 - x^4 - 5*x^3 - 2*x^2 - 9*x + 18)/(x - 1)^2 (as conjectured in comments). - Chai Wah Wu, Jan 26 2020