A238837 Numerators in the enumeration of the rationals by Czyz and Self.

0, 1, 1, 2, 3, 1, 2, 3, 5, 4, 5, 1, 2, 3, 3, 4, 7, 7, 8, 5, 7, 7, 8, 1, 2, 3, 3, 4, 5, 4, 5, 5, 9, 10, 11, 9, 12, 11, 13, 6, 9, 10, 11, 9, 12, 11, 13, 1, 2, 3, 3, 4, 5, 4, 5, 5, 7, 7, 8, 5, 7, 7, 8, 6, 11, 13, 14, 13, 17, 15, 18, 11, 16, 17, 19, 14, 19, 18, 21

Offset: 1

Author

N. J. A. Sloane, Mar 14 2014, following a suggestion from Kevin Ryde

Keywords

• nonn
• frac
• look

Comments

Denominators are A071766(n) for n >= 1.

Differs from A229742 by 1 at the integer rational positions n = 2^k because Czyz and Self only increment the last continued fraction term when there are two or more terms. So a(n) = A229742(n) - A209229(n) for n >= 1.

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Jerzy Czyz and William Self, The Rationals Are Countable: Euclid's Proof, The College Mathematics Journal, volume 34, number 5, November 2003, pages 367-369.

Crossrefs

Cf. A071766, A209229, A229742.

Programs

PARI

a(n) = my (w=[]); while (n, my (v=valuation(n,2)); w=concat(w, 1+v); n \= 2^(v+1)); w[#w]--; my (r=w[1] + (#w>1)); for (k=2, #w, r=w[k]+1/r); numerator(r) \\ Rémy Sigrist, Aug 25 2018

Extensions

More terms from Rémy Sigrist, Aug 25 2018