A334083 Integers m such that all binomial coefficients C(m,k), with 0<=k<=m, are practical numbers.

1, 2, 4, 16, 32, 64, 128, 256, 1024, 2048, 4096, 8192, 16384

Offset

1,2

Comments

Integers m such that A334082(m) = 0.

All terms are powers of 2, but this is not a sufficient condition since A334082(8) = 1.

Links

Table of n, a(n) for n=1..13.

Prog

(PARI) isok(n) = sum(k=0, n, !is_A005153(binomial(n, k))) == 0;
(Python)
from itertools import count, islice
from math import comb
from sympy import factorint
def A334083_gen(): # generator of terms
    for n in count(0):
        m, flag = 1<<n, True
        for k in range(1, m):
            c = comb(m, k)
            if c > 1:
                l = (~c & c-1).bit_length()
                if l>0:
                    P = (1<<l+1)-1
                    for p, e in factorint(c>>l).items():
                        if p > 1+P:
                            flag = False
                            break
                        P *= (p**(e+1)-1)//(p-1)
                else:
                    flag = False
                    break
        if flag:
            yield m
A334083_list = list(islice(A334083_gen(), 10)) # Chai Wah Wu, Jul 05 2023

Crossrefs

Cf. A005153 (practical numbers), A007318 (binomial coefficients).

Cf. A334082, A334084.

Sequence in context: A036345 A032464 A171381 * A274497 A145119 A081411

Adjacent sequences: A334080 A334081 A334082 * A334084 A334085 A334086

Keyword

nonn,more

Author

Michel Marcus, Apr 14 2020

Extensions

a(9) from Jinyuan Wang, Apr 14 2020

a(10)-a(13) from Chai Wah Wu, Jul 05 2023

Status

approved