A354255 Even numbers in A090252 in order of appearance.

2, 4, 8, 16, 26, 32, 64, 128, 206, 256, 478, 512, 998, 1024, 2048, 3134, 4096, 6514, 8192, 13942, 16384, 28894, 32768, 60518, 65536, 126634, 131072, 261398, 262144

Offset

1,1

Comments

The n-th even term in A090252 appears at index k <= A083329(n).

Conjecture: The indices of even numbers in A090252 are precisely the numbers {A083329(n), n >= 1}. See A090252 for discussion. - N. J. A. Sloane, May 22 2022

Taking logs to base 2 of these terms produces 1., 2., 3., 4., 4.700439718, 5., 6., 7., 7.686500527, 8., 8.900866807, 9., 9.962896004, 10., 11., 11.61378946, 12., 12.66932800, 13., 13.76714991, 14. - N. J. A. Sloane, Jun 01 2022

Links

Table of n, a(n) for n=1..29.

Prog

(Python)
from math import gcd, prod
from itertools import count, islice
def agen(): # generator of terms
    alst, aset, mink = [1], {1}, 2
    for n in count(2):
        k, s = mink, n - n//2
        prodall = prod(alst[n-n//2-1:n-1])
        while k in aset or gcd(prodall, k) != 1: k += 1
        alst.append(k); aset.add(k)
        if k%2 == 0: yield k
        while mink in aset: mink += 1
print(list(islice(agen(), 9))) # Michael S. Branicky, May 23 2022

Crossrefs

Cf. A083329, A090252, A247665, A248379, A353730, A354146, A354159.

Sequence in context: A302588 A348656 A354146 * A319385 A180249 A060957

Adjacent sequences: A354252 A354253 A354254 * A354256 A354257 A354258

Keyword

nonn,more

Author

Michael S. Branicky, May 21 2022

Extensions

a(14) from Michael S. Branicky, May 26 2022

a(15)-a(21) from Michael S. Branicky, Jun 01 2022 using gzipped b-file in A090252

a(22)-a(26) from Hugo van der Sanden, Jun 14 2022

a(27)-a(29) from Jinyuan Wang, Jul 15 2022

Status

approved