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A066044 Numbers k that are repdigits in more bases (smaller than k) than any smaller number. 11
1, 3, 7, 15, 24, 40, 60, 120, 180, 336, 360, 720, 840, 1260, 1440, 1680, 2520, 5040, 7560, 10080, 15120, 20160, 25200, 27720, 45360, 50400, 55440, 83160, 110880, 166320, 221760, 277200, 332640, 498960, 554400, 665280, 720720, 1081080, 1441440, 2162160, 2882880 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A repdigit has all digits the same in some base.

The number 3 isn't Brazilian (A125134) because 3 = 11_2 is an expansion of the type n = 11_(n-1), which is forbidden for Brazilian numbers. So, except for 3, all the integers in A066044 are highly Brazilian numbers (A329383). - Daniel Lignon, Dec 30 2019

REFERENCES

D. Lignon, Dictionnaire de (presque) tous les nombres entiers, Editions Ellipses, 2012, see p. 420. [In French.]

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..92

EXAMPLE

15 is in the sequence since 15 = 1111_2 = 33_4 = 11_14 and no smaller number is a repdigit in 3 different bases.

MATHEMATICA

a = 0 Range[100]; Do[ c = 1; k = 2; While[ k < n-1, If[ Length[ Union[ IntegerDigits[n, k]]] == 1, c++ ]; k++ ]; If[a[[c]] == 0, a[[c]] = n; Print[c, " = ", n]], {n, 1, 200000} ]

PROG

(PARI) okrepu3(b, target, lim) = {my(k = 3, nb = 0, x); while ((x=(b^k-1)/(b-1)) <= target, if (x==target, nb++); k++); nb; }

dge3(n, d) = {my(nb=0, ndi, limi); for (i=1, #d, ndi = n/d[i]; limi = sqrtint(ndi); for (k=d[i]+1, limi, nb += okrepu3(k, ndi, limi); ); ); nb; }

deq2(n, d) = {my(nb=0, nk); for (k=1, #d\2, nk = (n - d[k])/d[k]; if (nk > d[k], nb++); ); nb; }

beta23(n) = {if (n<3, return (0)); my(d=divisors(n)); deq2(n, d) + dge3(n, d); }

lista(nn) = {my(m = -1, nm); for (n=1, nn, if ((nm=beta23(n)) > m, print1(n, ", "); m = nm); ); } \\ Michel Marcus, Jul 13 2019

CROSSREFS

Cf. A066460, A329383.

Sequence in context: A283865 A283607 A001213 * A066460 A114221 A289828

Adjacent sequences:  A066041 A066042 A066043 * A066045 A066046 A066047

KEYWORD

nonn,base

AUTHOR

Erich Friedman, Dec 29 2001

EXTENSIONS

More terms from Robert G. Wilson v, Jan 02 2002

Offset changed to 1 by Giovanni Resta, Apr 05 2017

a(1) changed to 1 and new terms a(32)-a(41) from Giovanni Resta, Apr 05 2017

STATUS

approved

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Last modified February 24 06:13 EST 2020. Contains 332199 sequences. (Running on oeis4.)