login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 05:16 EDT 2024. Contains 371264 sequences. (Running on oeis4.)