A265403 Numbers m for which gcd{k=1..m-1} binomial(2*m, 2*k) = 2*m-1.

10, 12, 21, 22, 24, 30, 34, 36, 40, 51, 52, 55, 57, 69, 70, 76, 82, 84, 87, 90, 96, 99, 100, 106, 112, 114, 115, 117, 120, 129, 132, 136, 141, 142, 147, 154, 156, 159, 166, 174, 177, 180, 184, 187, 192, 195, 201, 205, 210, 216, 217, 220, 222, 225, 231, 232, 234, 240, 244, 246, 250, 252, 255, 261, 262, 274, 279, 282, 285, 286, 294, 297, 300

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..2014 from Antti Karttunen)

Mathematica

Select[Range@ 300, GCD @@ Array[Function[k, Binomial[2 #, 2 k]], {# - 1}] == 2 # - 1 &] (* Michael De Vlieger, Dec 11 2015 *)

Prog

(PARI) isok(n) = (n>1) && gcd(vector(n-1, k, binomial(2*n, 2*k))) == 2*n-1; \\ 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 A265403_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<<1)-1:
            yield n
A265403_list = list(islice(A265403_gen(), 50)) # Chai Wah Wu, May 04 2026

Crossrefs

Cf. A265388.

Cf. also A265402.

Sequence in context: A186438 A346678 A035284 * A215940 A368550 A337866

Adjacent sequences: A265400 A265401 A265402 * A265404 A265405 A265406

Keyword

nonn

Author

Antti Karttunen, Dec 08 2015

Status

approved