A261322 Non-repunit elements of A261020 in nonincreasing order.

21, 31, 41, 51, 61, 71, 81, 91, 421, 931, 3311, 5111, 5511, 7711, 8421, 9731, 9911, 311111, 444111, 711111, 777111, 993311, 8811111, 51111111, 55551111, 91111111, 93333311, 99311111, 99991111, 441111111, 6666611111, 7111111111, 9333311111, 411111111111, 555111111111, 771111111111, 777777111111, 911111111111

Offset: 1

Author

David A. Corneth, Aug 14 2015

Keywords

• nonn
• fini
• full
• base

Comments

Permutations of digits of all terms in this sequence are in A261020. There are 2403274 such permutations. About 38% (binomial(32,6) = 906192) of these permutations come from a(61) = 99999911111111111111111111111111.

On average, for every number of digits from 1 to 72, there's exactly one element.

Examples

			{1, 3, 9} forms a group under multiplication in Z/mZ for m = 13 and m = 26 (and no other values of m). m is the sum of digits of a term, so we can solve 9*x + 3*y + 1*z in {13, 26} for (x, y, z) >= (1, 1, 1). Solutions are (x, y, z) in {(1, 1, 1), (2, 2, 2), ..., (1, 1, 14)}. A solution (x, y, z) denotes a term starting with x nines, then followed by y threes, and then by z ones.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..72

Crossrefs

Cf. A261020.