A095415 Length of repunits of which the prime factor-digit-excess computed by A095414 equals 0.

2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 27, 31, 47, 59, 67, 71, 83, 113, 127, 139, 163, 197, 211, 229, 251, 263, 311, 317, 347, 421, 457, 461

Offset

1,1

Comments

541, 701, 857 are also terms. Conjecture: Except for the number 4, A046413 is a subsequence. Conjecture: except for the prime powers 9 and 27, all terms are prime. - Chai Wah Wu, Nov 03 2019

Sequence continues as 467?, 479?, 509?, 541, 557?, 571?, 577?, 593?, 599?, 617?, 643?, 647?, 661?, 673?, 683?, 691?, 701, 727?, 743?, 751?, 757?, 769?, 773?, 821?, 857, 863?, 887?, 911?, 967?, 971?, 977?, 991?, where ? marks uncertain/candidate terms. - Max Alekseyev, Apr 29 2022

Links

Table of n, a(n) for n=1..32.

Formula

Solutions to A095414(x) = 0.

Mathematica

d[1] = -1; d[n_] := Total[ IntegerLength /@ First /@ FactorInteger[(10^n - 1)/9]] - n; Select[ Range[67], d[#] == 0 &] (* Giovanni Resta, Jul 16 2018 *)

Crossrefs

A004023 is a subsequence.

Cf. A002275, A004023, A095370, A095407, A095413-A095418.

Sequence in context: A070566 A325623 A136327 * A326149 A301987 A353393

Adjacent sequences: A095412 A095413 A095414 * A095416 A095417 A095418

Keyword

nonn,more,base

Author

Labos Elemer, Jun 22 2004

Extensions

Data corrected and extended by Giovanni Resta, Jul 16 2018

a(29)-a(32) confirmed by Max Alekseyev, Apr 29 2022

Status

approved