A208682 Smallest m such that 2^m+m^2 = 0 mod prime(n), or 0 if no such m.

2, 1, 6, 0, 29, 22, 3, 5, 0, 94, 0, 34, 29, 39, 0, 12, 7, 68, 23, 0, 27, 0, 51, 55, 59, 298, 0, 77, 282, 30, 0, 357, 57, 227, 198, 0, 464, 49, 0, 112, 19, 106, 0, 37, 134, 0, 77, 0, 91, 128, 167, 0, 11, 187, 16, 0, 240, 0, 980, 10, 155, 52, 81, 0, 294, 284

Offset

1,1

Comments

It appears that a(n) = 0 iff p is 7 mod 8. [Charles R Greathouse IV, Mar 02 2012]

Links

Table of n, a(n) for n=1..66.

Example

a(3)=6 because prime(3)=5 and 2^6+6^2= 100=5*20
a(5)=29 because prime(5)=11 and 2^29+29^2=536871753=11*48806523

Mathematica

s={}; Do[p=Prime[n]; Do[If[Mod[2^m+m^2, p]<1, AppendTo[s, m]; Goto[nen]], {m, 100p}]; AppendTo[s, 0]; Label[nen], {n, 100}]; s

Prog

(PARI) a(n)=my(p=prime(n)); for(k=1, p*znorder(Mod(2, p)), if(Mod(2, p)^k+Mod(k, p)^2==0, return(k))); 0 \\ Charles R Greathouse IV, Mar 02 2012

Crossrefs

Sequence in context: A288505 A097407 A060480 * A094673 A196839 A295315

Adjacent sequences: A208679 A208680 A208681 * A208683 A208684 A208685

Keyword

nonn

Author

Zak Seidov, Mar 01 2012

Status

approved