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A291592 Number of bases for which 2^n-1 is a repdigit with at least 3 digits. 1
0, 0, 1, 1, 2, 2, 1, 2, 2, 2, 1, 4, 2, 2, 3, 3, 1, 4, 1, 4, 3, 2, 1, 6, 2, 2, 3, 4, 1, 6, 1, 4, 3, 2, 3, 7, 1, 2, 3, 6, 1, 6, 1, 4, 5, 2, 1, 8, 2, 4, 3, 4, 1, 6, 3, 6, 3, 2, 1, 10, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..62.

EXAMPLE

For n=3, 2^3-1 is 7; 7 is a repdigit with more than 3 digits only in base 2: 111_2. So a(3)=1.

For n=5, 2^5-1 is 31; 31 is a repdigit with more than 3 digits only in base 2 and 5: 11111_2 and 111_5 So a(5)=2.

MATHEMATICA

Table[With[{m = 2^n - 1}, Count[Range[2, Floor@ Sqrt@ m], _?(And[Length@ Union@ # == 1, Length@ # >= 3] &@ IntegerDigits[m, #] &) ]], {n, 40}] (* Michael De Vlieger, Aug 27 2017 *)

PROG

(PARI) nbr(n) = {nb = 0; fordiv(n, d, for (b=d+1, n, nd = 3; vd = [d, d, d]; while(fromdigits(vd, b) < n, nd ++; vd = vector(nd, k, d)); if ((x=fromdigits(vd, b)) == n, nb++); if ((x > n) && (nd == 3), break); ); ); nb; }

a(n) = nbr(2^n-1);

CROSSREFS

Cf. A000225, A290969.

Sequence in context: A279346 A168258 A116204 * A159905 A283735 A274534

Adjacent sequences:  A291589 A291590 A291591 * A291593 A291594 A291595

KEYWORD

nonn,more

AUTHOR

Michel Marcus, Aug 27 2017

STATUS

approved

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Last modified October 18 00:07 EDT 2019. Contains 328135 sequences. (Running on oeis4.)