A319216 -id:A319216 - cp's OEIS frontend

A319233 Numbers k such that k^2 + 1 divides 2^k + 4.

0, 1, 8, 28, 32, 128, 2048, 8192, 23948, 131072, 524288, 8388608, 536870912, 2147483648, 137438953472

Offset: 1

Altug Alkan, Sep 14 2018

This sequence corresponds to numbers k such that k^2 + 1 divides 2^k + 2^m where m = 2 (A247220 (m = 0), A319216 (m = 1)).

a(16) > 10^12. - Hiroaki Yamanouchi, Sep 17 2018

			32 = 2^5 is a term since (2^(2^5) + 2^2)/((2^5)^2 + 1) = 2^22 - 2^12 + 2^2.

Cf. A034785, A247220, A319216.

PARI
```
isok(n)=Mod(2, n^2+1)^n==-4;
```

a(15) from Hiroaki Yamanouchi, Sep 17 2018

A319245 Numbers k such that k^2 + 1 divides 2^k + 8.

Original entry on oeis.org

0, 1, 17, 37, 77, 197, 513, 993, 1837, 2617, 2637, 4097, 5437, 65537, 261633, 364137, 437837, 2097153, 16777217, 32761917, 54644032237, 68719476737, 137438953473, 1099511627777

Offset: 1

Altug Alkan, Sep 15 2018

Prime terms are 17, 37, 197, 2617, 5437, 65537, 437837, ...

Numbers t such that 2^t + 1 is a term are 4, 9, 12, 16, 21, 24, 36, 37, 40, 45, 49, 52, 57, 64, 69, 76, 84, 96, ...

Cf. A247220, A319216, A319233.

Select[Range[0, 9999], Divisible[2^# + 8, #^2 + 1] &] (* Alonso del Arte, Sep 16 2018 *)

PARI
```
isok(n)=Mod(2, n^2+1)^n==-8;
```

a(21)-a(24) from Hiroaki Yamanouchi, Sep 16 2018

cp's OEIS Frontend

A319233 Numbers k such that k^2 + 1 divides 2^k + 4.

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