A265402 Fixed points of A265388: numbers n for which gcd{k=1..n-1} binomial(2*n, 2*k) = n.

11, 17, 23, 29, 43, 47, 53, 59, 67, 71, 73, 83, 89, 101, 103, 107, 109, 113, 127, 131, 137, 149, 151, 163, 167, 173, 179, 191, 193, 197, 223, 227, 233, 239, 241, 251, 257, 263, 269, 277, 281, 283, 293, 311, 317, 347, 349, 353, 359, 373, 383, 389, 397, 401, 409, 419, 431, 433, 443, 449, 457, 461, 463, 467, 479, 487, 491, 503

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..1024 from Antti Karttunen)

Mathematica

Select[Range@ 504, GCD @@ Array[Function[k, Binomial[2 #, 2 k]], {# - 1}] == # &] (* Michael De Vlieger, Dec 11 2015 *)

Prog

(PARI) isok(n) = (n>1) && gcd(vector(n-1, k, binomial(2*n, 2*k))) == n; \\ Michel Marcus, Dec 08 2015, edited by Antti Karttunen, Dec 11 2015 (see A265388 for why).
(Python)
from math import prod
from itertools import count, islice
from sympy.ntheory.factor_ import digits
from sympy import primefactors
def A265402_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue, 1)):
        m = prod((p if sum(digits(n<<1, p)[1:])==2 else 1) for p in primefactors(n*((n<<1)-1)) if p>2)<<(not(n&-n)^n) if n>1 else 0
        if m==n:
            yield n
A265402_list = list(islice(A265402_gen(), 50)) # Chai Wah Wu, May 04 2026

Crossrefs

Fixed points of A265388. Cf. also A265403.

Sequence in context: A160129 A382051 A275682 * A145481 A006621 A337359

Adjacent sequences: A265399 A265400 A265401 * A265403 A265404 A265405

Keyword

nonn

Author

Antti Karttunen, Dec 08 2015

Status

approved