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A208682 Smallest m such that 2^m+m^2 = 0 mod prime(n), or 0 if no such m. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 5 16:53 EDT 2020. Contains 333245 sequences. (Running on oeis4.)