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A325659
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Smallest Brazilian composite in base n >= 2 which can be represented as a string of three or more 1's in this base.
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1
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15, 40, 21, 156, 259, 57, 585, 91, 111, 133, 1885, 183, 2955, 3616, 273, 5220, 343, 381, 8421, 9724, 507, 553, 14425, 651, 703, 20440, 813, 871, 931, 993, 1057, 37060, 1191, 1261, 1333, 1407, 56355, 1561, 1641, 70644, 1807, 1893, 1981, 2071, 2163, 2257, 2353, 2451, 127551
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OFFSET
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2,1
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COMMENTS
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Also the smallest Brazilian composite of the form (n^k - 1)/(n - 1) with k > 2.
For Mersenne numbers = (11...11)_2 = 2^k-1 in A000225, there is a smaller integer which is Brazilian prime: 7, so 7 is the first term of A285642 and another one is the smaller composite 15, so 15 is the first term of this sequence.
For numbers (11...11)_3 = (3^k-1)/2 in A003462, there is also a smaller integer which is Brazilian prime:13, so 13 is the second term of A285642 and another one is the smaller Brazilian composite: 40, so 40 is the second term of this sequence.
For numbers like (11...11)_4 = (4^k-1)/3, the terms are respectively 0 in A285642 because there is no Brazilian prime of this type and 21 for composite numbers of this sequence, and so on.
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LINKS
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Table of n, a(n) for n=2..50.
Wikipedia, Nombre brésilien
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EXAMPLE
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15 = (1111)_2, 40 = (1111)_3, 21 = (111)_4, 156 = (1111)_5.
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PROG
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(PARI) a(n) = {my(k=4, x); while (isprime(x=(n^(k-1)-1)/(n-1)), k++); x; } \\ Michel Marcus, May 17 2019
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CROSSREFS
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Subsequence of A053696, A220571, A325658.
Cf. A285642 (same with Brazilian primes).
Sequence in context: A126950 A091847 A062222 * A223432 A044092 A044473
Adjacent sequences: A325656 A325657 A325658 * A325660 A325661 A325662
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KEYWORD
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nonn,base
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AUTHOR
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Bernard Schott, May 12 2019
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EXTENSIONS
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More terms from Michel Marcus, May 17 2019
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STATUS
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approved
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