A325659 Smallest Brazilian composite in base n >= 2 which can be represented as a string of three or more 1's in this base.

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

Offset

2,1

Comments

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.

Links

Table of n, a(n) for n=2..50.

Wikipedia, Nombre brésilien

Example

15 = (1111)_2, 40 = (1111)_3, 21 = (111)_4, 156 = (1111)_5.

Prog

(PARI) a(n) = {my(k=4, x); while (isprime(x=(n^(k-1)-1)/(n-1)), k++); x; } \\ Michel Marcus, May 17 2019

Crossrefs

Subsequence of A053696, A220571, A325658.

Cf. A285642 (same with Brazilian primes).

Sequence in context: A062222 A369720 A369758 * A223432 A044092 A044473

Adjacent sequences: A325656 A325657 A325658 * A325660 A325661 A325662

Keyword

nonn,base

Author

Bernard Schott, May 12 2019

Extensions

More terms from Michel Marcus, May 17 2019

Status

approved