A048340 -id:A048340 - cp's OEIS frontend

A059711 Smallest base in which n is a repdigit.

2, 2, 3, 2, 3, 4, 5, 2, 3, 8, 4, 10, 5, 3, 6, 2, 7, 16, 5, 18, 9, 4, 10, 22, 5, 24, 3, 8, 6, 28, 9, 2, 7, 10, 16, 6, 8, 36, 18, 12, 3, 40, 4, 6, 10, 8, 22, 46, 7, 48, 9, 16, 12, 52, 8, 10, 13, 7, 28, 58, 9, 60, 5, 2, 15, 12, 10, 66, 16, 22, 9, 70, 11, 8, 36, 14, 18, 10, 12, 78, 3, 26, 40, 82, 11, 4

Offset: 0

Erich Friedman, Feb 19 2001

Numbers n such that a(n) < n - 1 correspond to Brazilian numbers (A125134); conversely, positive numbers n such that a(n) >= n - 1 correspond to A220570. - Rémy Sigrist, Apr 04 2018

			a(13) = 3 since 13 in base 3 is 111.

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Cf. A010785, A125134, A048328, A048329, A048330, A048331, A048332, A048333, A048334, A048335, A048336, A048337, A048338, A048339, A048340, A220570.

a(n) = for (b=2, oo, if (#Set(digits(n, b))<=1, return (b))) \\ Rémy Sigrist, Apr 04 2018

From Rémy Sigrist, Apr 04 2018: (Start)
a(n) <= n - 1 for any n >= 3.
a(2^n-1) = 2 for any n >= 0.
a(A048328(n)) <= 3 for any n >= 0.
a(A048329(n)) <= 4 for any n >= 0.
a(A048330(n)) <= 5 for any n >= 0.
a(A048331(n)) <= 6 for any n >= 0.
a(A048332(n)) <= 7 for any n >= 0.
a(A048333(n)) <= 8 for any n >= 0.
a(A048334(n)) <= 9 for any n >= 0.
a(A010785(n)) <= 10 for any n >= 0.
a(A048335(n)) <= 11 for any n >= 0.
a(A048336(n)) <= 12 for any n >= 0.
a(A048337(n)) <= 13 for any n >= 0.
a(A048338(n)) <= 14 for any n >= 0.
a(A048339(n)) <= 15 for any n >= 0.
a(A048340(n)) <= 16 for any n >= 0.
(End)

Example clarified by Harvey P. Dale, Oct 11 2015

Terms a(0) = 2, a(1) = 2 and a(2) = 3 prepended by Rémy Sigrist, Apr 04 2018

A226542 Primes p such that p - 1 can be represented as a repdigit number in some base < p which is a power of two.

Original entry on oeis.org

11, 19, 37, 43, 67, 103, 131, 137, 199, 239, 293, 331, 397, 439, 463, 521, 547, 661, 683, 727, 859, 911, 991, 1033, 1093, 1171, 1291, 1301, 1543, 1549, 1951, 2053, 2081, 2341, 2731, 2861, 3079, 3121, 3251, 3511, 3613, 3823, 4099, 4129, 4229, 4903, 5419, 6151

Offset: 1

Arkadiusz Wesolowski, Jun 10 2013

It is believed that this is a supersequence of A001220 (Wieferich primes).

			103 is in the sequence because it is prime and 102 = 66 (base 16).
463 is in the sequence because it is prime and 462 = ee (base 32).
7 is not in the sequence since 6 = 6 (base 8) and 8 > 7.

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000
John Blythe Dobson, A note on the two known Wieferich Primes
Wells Johnson, On the nonvanishing of Fermat quotients (mod p), Journal f. die reine und angewandte Mathematik 292, (1977): 196-200.
Wikipedia, Repdigit

Cf. A001220, A010785, A048329, A048333, A048340.

lst = {}; r = 13; Do[If[PrimeQ[p] && Length@Union@IntegerDigits[p - 1, 2^b] == 1, AppendTo[lst, p]], {b, 2, r - 1}, {p, 2^b + 1, 2^r - 1, 2}]; Union[lst]

cp's OEIS Frontend

A059711 Smallest base in which n is a repdigit.

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