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A106310
Primes p such that p^2 divides some T(k), yet p does not divide any T(j) for any j<k, where T(n) is the n-th tribonacci number (A000073).
0
47, 617, 2693
OFFSET
1,1
COMMENTS
No other p < 10^6. For Fibonacci numbers, A000045, there are no known primes with this property.
EXAMPLE
47 is here because the 29th tribonacci number, 15902591, is the first tribonacci number divisible by 47 and 47^2 also divides it. Similarly, 617^2 divides T(409) and 2693^2 divides T(10553).
MATHEMATICA
FibonacciZero[n_, kMax_, m_] := Module[{a, s, k}, a=Join[{1}, Table[0, {n-1}]]; a=Mod[a, m]; k=0; While[k++; s=Mod[Plus@@a, m]; a=RotateLeft[a]; a[[n]]=s; s>0&&k<kMax]; If[s==0, k, -1]]; Do[p=Prime[n]; zero=FibonacciZero[3, Infinity, p]; If[zero==FibonacciZero[3, zero, p^2], Print[{p, zero}]], {n, 1000}]
CROSSREFS
Sequence in context: A142253 A142577 A098226 * A163709 A244880 A101793
KEYWORD
bref,hard,more,nonn
AUTHOR
T. D. Noe, May 17 2005
STATUS
approved