[seqfan] Two-and-five conjecture

[Vladimir Shevelev]

Dear Seqfans,

For a prime p, denote by s(p,k) the odd part of the digital sum of p^k.
Let k_n be the smallest k such that s(p,k) is divisible by prime(n), n>=3.
I and Peter Moses conjecture that, for every n>=3, k_n=k_n(p) exists 
for every p, and, moreover, the equality s(p,k_n) = prime(n) holds for
every such n, if and only if p=2 or 5.
For connected sequences, see A251964 and A252280-A252283.

Best regards,
Vladimir