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

1,4

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.

Prog

(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

Crossrefs

Cf. A071766, A209229, A229742.

Sequence in context: A174981 A067280 A167157 * A309940 A081514 A109206

Adjacent sequences: A238834 A238835 A238836 * A238838 A238839 A238840

Keyword

nonn,frac,look

Author

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

Extensions

More terms from Rémy Sigrist, Aug 25 2018

Status

approved