A252606 Numbers j such that j + 2 divides 2^j + 2.

3, 4, 16, 196, 2836, 4551, 5956, 25936, 46775, 65536, 82503, 540736, 598816, 797476, 1151536, 3704416, 4290771, 4492203, 4976427, 8095984, 11272276, 13362420, 21235696, 21537831, 21549347, 29640832, 31084096, 42913396, 49960912, 51127259, 55137316, 56786087, 60296571, 70254724, 70836676

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 03 2015

Keywords

• nonn
• hard

Comments

Numbers j such that (2^j + 2)/(j + 2) is an integer. Numbers j such that (2^j - j)/(j + 2) is an integer.

From Robert Israel, Apr 09 2015: (Start)

The even members of this sequence (4, 16, 196, 2836, ...) are the numbers 2*k-2 where k>=3 is odd and 4^k == -8 (mod k).

The odd members of this sequence (3, 4551, 46775, 82503, ...) are the numbers k-2 where k>=3 is odd and 2^k == -8 (mod k). (End)

2^m is in this sequence for m = (2, 4, 16, 36, 120, 256, 456, 1296, 2556, ...), with the subsequence m = 2^k, k = (1, 2, 4, 8, 16, ...). - M. F. Hasler, Apr 09 2015

Examples

			3 is in this sequence because (2^3 + 2)/(3 + 2) = 2.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..78

Crossrefs

Cf. A001477, A004273, A004275, A081765, A213382, A251603.

Programs

Magma

[n: n in [0..1200000] | Denominator((2^n+2)/(n+2)) eq 1];

Maple

select(t -> 2 &^t + 2 mod (t + 2) = 0, [$1..10^6]); # Robert Israel, Apr 09 2015

Mathematica

Select[Range[10^6],IntegerQ[(2^#+2)/(#+2)]&] (* Ivan N. Ianakiev, Apr 17 2015 *)

PARI

for(n=1,10^5,if((2^n+2)%(n+2)==0,print1(n,", "))) \\ Derek Orr, Apr 05 2015

PARI

is(n)=Mod(2,n+2)^n==-2 \\ M. F. Hasler, Apr 09 2015

Python

A252606_list = [n for n in range(10**4) if pow(2, n, n+2) == n] # Chai Wah Wu, Apr 16 2015

Extensions

a(17)-a(22) from Tom Edgar, Mar 03 2015

More terms from Chai Wah Wu, Apr 16 2015