A328899 -id:A328899 - cp's OEIS frontend

A095371 Number of distinct prime factors of record setting repunits (A328899).

0, 1, 2, 5, 7, 8, 10, 13, 14, 20, 21, 22, 26, 29, 32, 33, 34, 35, 40, 44, 55, 56, 63

Offset: 1

Labos Elemer, Jun 04 2004

Conjecture: a(24) = 73, a(25) = 94, a(26) = 99, a(27) >= 107, a(28) >= 127, a(29) >= 136, a(30) >= 140, a(31) >= 151, a(32) >= 159, a(33) >= 163, a(34) >= 178, a(35) >= 184, a(36) >= 213, a(37) >= 214. - Chai Wah Wu, Nov 01 2019

Cf. A067063, A003020, A001221, A002275, A095370, A004023.

r[n_] := (10^n-1)/9; L = {}; bst = -1; Do[v = PrimeNu[r[n]]; If[v > bst, bst = v; AppendTo[L, v]], {n, 60}]; L
(* or, based on the b-file of A095370: *)
w = Last /@ Cases[Import["https://oeis.org/A095370/b095370.txt", "Table"], {Integer, _Integer}]; L = {}; bst = -1; Do[ If[j > bst, AppendTo[L, bst = j]], {j, w}]; L (* _Giovanni Resta, Oct 30 2019 *)

Data corrected by Ray Chandler and N. J. A. Sloane, May 03 2017
Name edited by Giovanni Resta, Oct 30 2019
a(20)-a(21) from Chai Wah Wu, Oct 30 2019
a(22)-a(23) from Chai Wah Wu, Nov 01 2019

A095416 Length of smallest repunit of which the prime factor-digit-excess computed by A095414 equals n.

Original entry on oeis.org

2, 4, 6, 12, 24, 32, 30, 80, 96, 60, 84, 126, 120, 200, 168, 264, 210, 252

Offset: 0

Labos Elemer, Jun 22 2004

a(18), a(19) > 322. a(20) = 300. - Giovanni Resta, Jul 19 2018

a(A095371(n)-1) >= A328899(n). a(18) <= 440, a(19) <= 336, a(21) <= 624, a(22) <= 560, a(23) <= 480, a(24) <= 540, a(25) <= 720, a(26) <= 612, a(27) <= 420, a(28) <= 600, a(30) = 1050, a(31) <= 660, a(32) <= 1400, a(33) <= 900, a(34) <= 1020, a(35) <= 1500, a(36) <= 1380, a(37) <= 840, a(48) <= 1260, a(50) <= 1680. - Chai Wah Wu, Nov 03 2019

			n=60: concatenated p-set for 60th-repunit is:
371113313741611012112412712161354190919901279612906161418890139526741,
its length=69, so excess=9, 60 is the smallest such repunit

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

a(n) = Min{x; A095414(x)=n}.

Edited by Charles R Greathouse IV, Aug 03 2010
Data corrected and extended by Giovanni Resta, Jul 19 2018
a(0) from Chai Wah Wu, Nov 03 2019

cp's OEIS Frontend

A095371 Number of distinct prime factors of record setting repunits (A328899).

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