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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

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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