A005347 First differences of A005579. (Formerly M0690)

1, 1, 2, 3, 5, 8, 13, 20, 34, 53, 88, 143, 236, 387, 641, 1061, 1763, 2937, 4903, 8202, 13750, 23095, 38850, 65461, 110465, 186665, 315827, 535011, 907341, 1540416, 2617782, 4452846, 7581016, 12917486, 22027745, 37591270, 64196610

Offset

1,3

Comments

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

References

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

Links

Table of n, a(n) for n=1..37.

R. K. Guy, Letter to N. J. A. Sloane, 1988-04-12 (annotated scanned copy)

R. K. Guy, Letters to N. J. A. Sloane, 1986-88

R. K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20.

R. K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]

Richard Laatsch, Measuring the abundancy of integers, Mathematics Magazine 59 (2) (1986) 84-92.

Formula

a(n) = A005579(n+1) - A005579(n) - T. D. Noe, May 08 2006

Mathematica

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 *)

Crossrefs

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

Sequence in context: A080106 A293644 A158415 * A100582 A193616 A273715

Adjacent sequences: A005344 A005345 A005346 * A005348 A005349 A005350

Keyword

nonn,nice

Author

N. J. A. Sloane, R. K. Guy, Apr 12 1988

Extensions

More terms from Harvey P. Dale, Aug 07 2013

Status

approved