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

1,1

Comments

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

Links

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

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

Example

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.

Crossrefs

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

Sequence in context: A226971 A281918 A186129 * A265738 A151741 A090064

Adjacent sequences: A284669 A284670 A284671 * A284673 A284674 A284675

Keyword

nonn

Author

Seiichi Manyama, Apr 01 2017

Status

approved