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A112714
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Numbers of the form k*2^m-1 with k<2^m and k odd.
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6
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1, 3, 7, 11, 15, 23, 31, 39, 47, 55, 63, 79, 95, 111, 127, 143, 159, 175, 191, 207, 223, 239, 255, 287, 319, 351, 383, 415, 447, 479, 511, 543, 575, 607, 639, 671, 703, 735, 767, 799, 831, 863, 895, 927, 959, 991, 1023, 1087, 1151, 1215, 1279, 1343, 1407
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OFFSET
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1,2
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..10000
Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, p. 38.
Eric Weisstein's World of Mathematics, Proth Numbers
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EXAMPLE
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a(4)=7 because 7 = 1*2^3 - 1, with 1 < 2^3, and it is the fourth number of this form.
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MAPLE
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N:= 2000: # to get all terms <= N
sort(convert({seq(seq(k*2^m-1, k=1..min((N+1)/2^m, 2^m-1), 2), m=1..ilog2(N+1))}, list)); # Robert Israel, May 23 2017
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MATHEMATICA
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Take[Sort@Flatten@Table[k*2^m - 1, {m, 0, 10}, {k, 1, 2^m - 1, 2}], 53] (* Robert G. Wilson v, Jan 02 2006 *)
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PROG
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(PARI) for(n=2, 8, for(k=2^(n-2)+1, 2^n, print1(k*2^n-1", "))) \\ Note that the first two terms (1, 3) are not computed
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CROSSREFS
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Cf. A080075.
Sequence in context: A279106 A172306 A309274 * A327330 A231348 A194444
Adjacent sequences: A112711 A112712 A112713 * A112715 A112716 A112717
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KEYWORD
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easy,nonn
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AUTHOR
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Jose Brox (tautocrona(AT)terra.es), Dec 31 2005
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STATUS
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approved
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