A273672 Permutation of natural numbers induced by looking up the position of fraction A270418(n)/A270419(n) from the full Stern-Brocot tree A007305(n+1)/A047679(n-1).

1, 3, 7, 15, 31, 63, 127, 2, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 1048575, 2097151, 4194303, 8388607, 6, 33554431, 67108863, 4, 268435455, 536870911, 1073741823, 2147483647, 128, 8589934591, 17179869183, 34359738367, 68719476735, 137438953471, 274877906943, 549755813887, 14

Offset: 1

Author

Antti Karttunen, May 27 2016

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1024
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A273671.

Cf. A270418, A270419.

Cf. also A007305, A047679.

Programs

PARI

A065620(n, c=1) = sum(i=0, logint(n+!n, 2), if(bittest(n, i), (-1)^c++<A065620
SBtree_index(r) = { my(m=numerator(r),n=denominator(r),z=1); while(m!=n, if(mA273672(n) = { n=factor(n); n[, 2] = apply(A065620, n[, 2]); SBtree_index(factorback(n)); }; \\ Antti Karttunen, Mar 07 2020, based also on M. F. Hasler's code in A270418 and A270419

Scheme

(define (A273672 n) (SBtree_index (A270418 n) (A270419 n)))
(define (SBtree_index m n) (let loop ((m m) (n n) (z 1)) (cond ((= m n) z) ((< m n) (loop m (- n m) (+ z z))) (else (loop (- m n) n (+ z z 1))))))