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 A064896 Numbers of the form (2^{mr}-1)/(2^r-1) for positive integers m, r. 16
 1, 3, 5, 7, 9, 15, 17, 21, 31, 33, 63, 65, 73, 85, 127, 129, 255, 257, 273, 341, 511, 513, 585, 1023, 1025, 1057, 1365, 2047, 2049, 4095, 4097, 4161, 4369, 4681, 5461, 8191, 8193, 16383, 16385, 16513, 21845, 32767, 32769, 33825, 37449, 65535, 65537 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Binary expansion of n consists of single 1's diluted by (possibly empty) equal-sized blocks of 0's. A064894(a(n)) = A056538(n) According to Stolarsky's Theorem 2.1, all numbers in this sequence are sturdy numbers; this sequence is a subsequence of A125121. - T. D. Noe, Jul 21 2008 LINKS T. D. Noe, Table of n, a(n) for n=1..1000 T. Chinburg and M. Henriksen, Sums of k-th powers in the ring of polynomials with integer coefficients, Acta Arithmetica, 29 (1976), 227-250. K. B. Stolarsky, Integers whose multiples have anomalous digital frequencies, Acta Arithmetica, 38 (1980), 117-128. EXAMPLE 73 is included because it is 1001001 in binary, whose 1's are diluted by blocks of two 0's. MAPLE f := proc(p) local m, r, t1; t1 := {}; for m from 1 to 10 do for r from 1 to 10 do t1 := {op(t1), (p^(m*r)-1)/(p^r-1)}; od: od: sort(convert(t1, list)); end; f(2); # very crude! # Alternative: N:= 10^6: # to get all terms <= N A:= sort(convert({1, seq(seq((2^(m*r)-1)/(2^r-1), m=2..1/r*ilog2(N*(2^r-1)+1)), r=1..ilog2(N-1))}, list)); # Robert Israel, Jun 12 2015 PROG (PARI) lista(nn) = {v = [1]; x = (2^nn-1); for (m=2, nn, r = 1; while ((y = (2^(m*r)-1)/(2^r-1)) <=x, v = Set(concat(v, y)); r++); ); v; } \\ Michel Marcus, Jun 12 2015 CROSSREFS Cf. A064894, A056538. Cf. A076270 (k=3), A076275 (k=4), A076284 (k=5), A076285 (k=6), A076286 (k=7), A076287 (k=8), A076288 (k=9), A076289 (k=10). Primes in this sequence: A245730. Sequence in context: A163410 A329419 A235264 * A076188 A265852 A335132 Adjacent sequences: A064893 A064894 A064895 * A064897 A064898 A064899 KEYWORD base,easy,nonn AUTHOR Marc LeBrun, Oct 11 2001 STATUS approved

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Last modified December 8 11:46 EST 2023. Contains 367678 sequences. (Running on oeis4.)