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

1,1

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.

Links

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

Example

{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.

Crossrefs

Cf. A261020.

Sequence in context: A376294 A067599 A342838 * A123846 A336383 A168000

Adjacent sequences: A261319 A261320 A261321 * A261323 A261324 A261325

Keyword

nonn,fini,full,base

Author

David A. Corneth, Aug 14 2015

Status

approved