A265394 Positions of records in A265388.

1, 2, 3, 6, 7, 15, 19, 31, 37, 79, 97, 139, 157, 199, 211, 229, 271, 307, 331, 337, 367, 379, 439, 499, 547, 577, 601, 607, 619, 661, 691, 727, 811, 829, 877, 937, 967, 997, 1009, 1069, 1171, 1237, 1279, 1297, 1399, 1429, 1459, 1531, 1609, 1627, 1657, 1759, 1867, 2011, 2029, 2089, 2131, 2137, 2179, 2221, 2281, 2311

Offset

1,2

Comments

Question: Apart from a(1)=1, a(4)=6 and a(6)=15, are all other terms primes? See also comments in A265395 & A265396.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..192 from Antti Karttunen)

Mathematica

DeleteDuplicates[Table[{n, GCD@@Array[Binomial[2 n, 2 #]&, {n-1}]}, {n, 2350}], GreaterEqual[ #1[[2]], #2[[2]]]&][[All, 1]] (* Harvey P. Dale, Jul 19 2022 *)

Prog

(PARI) lista(nn) = {r = 0; for (n=1, nn, nr = gcd(vector(n-1, k, binomial(2*n, 2*k))); if (nr > r, print1(n, ", "); r = nr); ); } \\ Michel Marcus, Dec 08 2015
(Python)
from math import prod
from itertools import count, islice
from sympy.ntheory.factor_ import digits
from sympy import primefactors
def A265394_gen(): # generator of terms
    c = -1
    for n in count(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>c:
            yield n
            c = m
A265394_list = list(islice(A265394_gen(), 20)) # Chai Wah Wu, May 04 2026

Crossrefs

Cf. A265388.

Cf. A265395 (gives the record values), A265396.

Sequence in context: A245479 A294524 A032882 * A125167 A137604 A034901

Adjacent sequences: A265391 A265392 A265393 * A265395 A265396 A265397

Keyword

nonn

Author

Antti Karttunen, Dec 08 2015

Status

approved