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A066044
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Numbers k that are repdigits in more bases (smaller than k) than any smaller number.
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5
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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
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OFFSET
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1,2
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COMMENTS
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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 terms here are highly Brazilian numbers (A329383). - Daniel Lignon, Dec 30 2019
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REFERENCES
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D. Lignon, Dictionnaire de (presque) tous les nombres entiers, Editions Ellipses, 2012, see p. 420. [In French.]
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LINKS
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EXAMPLE
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15 is in the sequence since 15 = 1111_2 = 33_4 = 11_14 and no smaller number is a repdigit in 3 different bases.
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MATHEMATICA
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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} ]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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a(1) changed to 1 and new terms a(32)-a(41) from Giovanni Resta, Apr 05 2017
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STATUS
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approved
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