A005347 First differences of A005579.

1, 1, 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: 0

Author

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

Keywords

• nonn
• nice

Comments

This is example 42 in Guy's paper. a(2)-a(8) 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

• Amiram Eldar, Table of n, a(n) for n = 0..43
• Richard K. Guy, Letter to N. J. A. Sloane, 1988-04-12 (annotated scanned copy).
• Richard K. Guy, Letters to N. J. A. Sloane, 1986-88.
• Richard K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20.
• Richard 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.

Crossrefs

Cf. A000045, A005579.

Programs

Mathematica

prod = Interval[1]; k = k0 = 0; Join[{1, 1}, 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 *)

Formula

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

Extensions

More terms from Harvey P. Dale, Aug 07 2013

Offset changed to 0, a(0) prepended, and a(1) inserted by Amiram Eldar, Apr 18 2025