A261179 a(n) is the prime(n)-th term of Stern-Brocot sequence, A002487.

1, 2, 3, 3, 5, 5, 5, 7, 7, 7, 5, 11, 11, 13, 9, 13, 11, 9, 11, 13, 15, 13, 19, 17, 11, 19, 17, 21, 19, 13, 7, 13, 19, 23, 29, 25, 23, 25, 27, 31, 29, 31, 13, 13, 25, 23, 31, 17, 23, 27, 25, 19, 17, 17, 9, 19, 27, 21, 37, 31, 35, 41, 41, 37, 33, 29, 49, 37, 49, 41, 27, 41, 33, 41, 31, 15, 31, 39, 33, 41, 41, 49, 37, 35, 41, 39, 19, 37, 41, 31, 43, 23, 31, 37, 27, 23, 15, 27

Offset

1,2

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) = numerator of R(prime(n)). - The original name of this 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 numerator of R(prime(n)) reduces to just A002487(prime(n)). - Antti Karttunen, Dec 02 2025]

Apart from a(2) = A002487(A000040(2)) = A002487(3) = 2, all other terms are odd because A002487(n) is even if and only if n is a multiple of 3. - 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(A000040(n)) = A001222(A277316(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]]] (* 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); };
A261179(n) = A002487(prime(n)); \\ Antti Karttunen, Dec 02 2025

Crossrefs

Cf. A000040, A001222, A002487, A261273 (denominators), A277316.

Sequence in context: A256405 A130149 A053046 * A066658 A005145 A280740

Adjacent sequences: A261176 A261177 A261178 * A261180 A261181 A261182

Keyword

nonn,easy,frac

Author

James Kirk Winkler, Aug 10 2015

Extensions

Definition simplified by Antti Karttunen, Dec 02 2025

Status

approved