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A306401 The smallest integer k | 2^k + 1 such that omega(k) = n. 1

%I #18 Oct 13 2023 07:51:51

%S 1,3,171,97641,143239347,626958621819,5519116747872657,

%T 50428169725312467009,2073253341916771456141017,

%U 163345411049596672714982306379,14245516643046375424146321921618969,1929313055517699762818408816810621828577,269106372922775316017200116995195964515405691,38930811651619136642260289325344014598550195099897

%N The smallest integer k | 2^k + 1 such that omega(k) = n.

%C Conjecture: a(n) | a(n+1).

%C Conjecture does not hold in general and first time fails at n=26, then it fails at n=47, n=72, and so on. - _Max Alekseyev_, Oct 12 2023

%H Max Alekseyev, <a href="/A306401/b306401.txt">Table of n, a(n) for n = 0..100</a>

%o (PARI) v = readvec("v006521.txt");

%o a(n) = {k=1; while(omega(v[k]) != n, k++); v[k]; };

%o (PARI) a(n) = my(m=1); while((Mod(2, m)^m!=-1) || (omega(m)!=n), m++); m; \\ _Michel Marcus_, Feb 16 2019

%Y Cf. A006521, A001221 (omega).

%K nonn

%O 0,2

%A _Jinyuan Wang_, Feb 15 2019

%E a(6)-a(10) confirmed, terms (11) onward added by _Max Alekseyev_, Oct 12 2023

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Last modified August 13 16:28 EDT 2024. Contains 375144 sequences. (Running on oeis4.)