A261273 a(n) is the (prime(n)+1)-th term of Stern-Brocot sequence, A002487.

2, 1, 2, 1, 2, 3, 4, 3, 2, 4, 1, 7, 8, 5, 2, 8, 4, 5, 5, 4, 11, 3, 8, 12, 9, 12, 5, 8, 11, 10, 1, 6, 14, 9, 18, 7, 13, 11, 8, 18, 12, 19, 2, 11, 16, 7, 13, 3, 10, 17, 18, 4, 13, 6, 8, 6, 16, 5, 23, 22, 13, 26, 17, 10, 23, 16, 19, 29, 18, 23, 22, 12, 7, 25, 11, 2, 20, 23, 26, 29, 18, 31, 8, 27, 11, 14, 16, 27, 24

Offset

1,1

Comments

Take the list of positive rationals {R(n): n>=1} in the order defined by Calkin and Wilf (Recounting the Rationals, 1999); a(n) = denominator of R(prime(n)). - The original definition of the sequence.

The list of rationals {R(n)} is essentially given by A002487(n)/A002487(n+1).

As two adjacent terms of A002487 are always relatively prime, the denominator of R(prime(n)) reduces to A002487(1+prime(n)). - Antti Karttunen, Dec 02 2025

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Neil Calkin and Herbert S. Wilf, Recounting the rationals, Amer. Math. Monthly (2000) Vol. 107, No. 4, 360-363.

Index entries for sequences related to Stern's sequences.

Formula

a(n) = A002487(A008864(n)) = A002487(1+prime(n)). - Antti Karttunen, Dec 02 2025

Mathematica

A002487[n_] := A002487[n] = Which[n <= 1, n, OddQ[n], A002487[(n-1)/2] + A002487[(n+1)/2], True, A002487[n/2]];
Map[A002487, Prime[Range[100]] + 1] (* Paolo Xausa, Dec 03 2025 *)

Prog

(PARI)
A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); };
A261273(n) = A002487(1+prime(n)); \\ Antti Karttunen, Dec 02 2025

Crossrefs

Cf. A002487, A008864, A261179 (numerators).

Sequence in context: A303780 A234022 A389352 * A097454 A139803 A058746

Adjacent sequences: A261270 A261271 A261272 * A261274 A261275 A261276

Keyword

nonn,easy,frac

Author

James Kirk Winkler, Aug 13 2015

Extensions

Definition simplified by Antti Karttunen, Dec 02 2025

Status

approved