A005347 - OEIS

%I M0690 #37 Jun 26 2017 23:01:20

%S 1,1,2,3,5,8,13,20,34,53,88,143,236,387,641,1061,1763,2937,4903,8202,

%T 13750,23095,38850,65461,110465,186665,315827,535011,907341,1540416,

%U 2617782,4452846,7581016,12917486,22027745,37591270,64196610

%N First differences of A005579.

%C This is example 42 in Guy's paper. The first seven terms are the same as the Fibonacci sequence A000045. Subsequent terms deviate from Fibonacci. - _T. D. Noe_, May 08 2006

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H R. K. Guy, <a href="/A000081/a000081.pdf">Letter to N. J. A. Sloane, 1988-04-12</a> (annotated scanned copy)

%H R. K. Guy, <a href="/A005347/a005347_1.pdf">Letters to N. J. A. Sloane, 1986-88</a>

%H R. K. Guy, <a href="http://www.jstor.org/stable/2691503">The Second Strong Law of Small Numbers</a>, Math. Mag, 63 (1990), no. 1, 3-20.

%H R. K. Guy, <a href="/A005347/a005347.pdf">The Second Strong Law of Small Numbers</a>, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]

%H Richard Laatsch, <a href="http://www.jstor.org/stable/2690424">Measuring the abundancy of integers</a>, Mathematics Magazine 59 (2) (1986) 84-92.

%F a(n) = A005579(n+1) - A005579(n) - _T. D. Noe_, May 08 2006

%t prod = Interval[1]; k = k0 = 0; Table[While[Max[prod] <= n, k++; p = Prime[k]; prod = N[prod*p/(p - 1), 30]]; If[Min[prod] > n, If[k > 2, Print[k - k0] ]; k0 = k; k, "too few digits"], {n, 2, 39}] // Differences (* _Jean-François Alcover_, Oct 07 2016, using _T. D. Noe_'s code for A005579 *)

%Y Cf. A005579 (least number of distinct prime factors in even numbers having an abundancy index >n).

%K nonn,nice

%O 1,3

%A _N. J. A. Sloane_, _R. K. Guy_, Apr 12 1988

%E More terms from _Harvey P. Dale_, Aug 07 2013