A157806 Absolute value of the difference between numerator and denominator of fractions arranged by Cantor's ordering (1/1, 2/1, 1/2, 1/3, 3/1, 4/1, 3/2, 2/3, 1/4, 1/5, 5/1, 6/1, ...) with equivalent fractions removed.

0, 1, 1, 2, 2, 3, 1, 1, 3, 4, 4, 5, 3, 1, 1, 3, 5, 6, 2, 2, 6, 7, 5, 1, 1, 5, 7, 8, 4, 4, 8, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 10, 2, 2, 10, 11, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 11, 12, 8, 4, 4, 8, 12, 13, 11, 7, 1, 1, 7, 11, 13, 14, 10, 6, 2, 2, 6, 10, 14, 15, 13, 11

Offset: 0

Author

Ron R. King, Mar 07 2009

Keywords

• nonn
• look

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..10000

Crossrefs

Sum of numerator and denominator is given by A038567.

Programs

PARI

seq(n)={my(L=List(), r=1, k=1); while(#L<=n, if(k==r, r++; k=0); k++; if(gcd(k,r-k)==1, listput(L, abs(r-2*k)))); Vec(L)} \\ Andrew Howroyd, Feb 03 2021

Extensions

Terms a(56) and beyond from Andrew Howroyd, Feb 03 2021