A341887 a(n) = A341886(n)/2; numbers k such that A307437(k) is even.

256, 512, 1024, 2816, 4096, 5632, 8192, 11264, 27136, 28928, 48896, 54272, 61184, 65536, 75008, 82688, 84992, 90112, 94464, 97792, 105216, 122368, 124160, 128000, 138240, 139520, 150016, 158720, 166656, 167168, 167936, 168704, 176128, 183808, 185856, 195584

Offset: 1

Author

Jianing Song, Feb 22 2021

Keywords

• nonn
• hard

Comments

Indices of even terms in A307437; A341886 is the main entry.

Numbers k such that 2^k is a term: 8, 9, 10, 12, 13, 16, 18, 19, 20, 21, 22, 23, ... Are all sufficiently large powers of 2 terms? - Chai Wah Wu, Feb 24 2021

We don't know. From the comments in A341886, 2^k is a term if and only if t*2^(k+1)+1 is composite for t = 1, 2, 3. But we don't know if there are infinitely many Fermat primes. - Jianing Song, Feb 26 2021

All terms are divisible by 256. See my comment in A341886. - Jianing Song, Feb 27 2021

Examples

			psi(2048) = 512 is divisible by 2*256, and there is no odd m < 2048 such that 2*256 | psi(m), so 256 is a term.
psi(47104) = 5632 is divisible by 2*2816, and there is no m < 47104 such that 2*2816 | psi(m), so 2816 is a term.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A002322, A307437, A341886.

Programs

PARI

forstep(n=2, 10000, 2, if(A307437(n)%2==0, print1(n, ", "))) \\ see A307437 for its program

Extensions

a(9)-a(20) from Michel Marcus, Feb 24 2021

a(21)-a(36) from Chai Wah Wu, Feb 24 2021