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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

No other p < 10^6. For Fibonacci numbers, A000045, there are no known primes with this property.

LINKS

Table of n, a(n) for n=1..3.

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

Adjacent sequences:  A106307 A106308 A106309 * A106311 A106312 A106313

KEYWORD

bref,hard,more,nonn

AUTHOR

T. D. Noe, May 17 2005

STATUS

approved

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Last modified September 20 12:31 EDT 2017. Contains 292271 sequences.