A106310 Primes p such that p^2 divides some T(k), yet p does not divide any T(j) for any jA000073).

47, 617, 2693

Offset: 1

Author

T. D. Noe, May 17 2005

Keywords

• bref
• hard
• more
• nonn

Comments

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

Examples

			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).
		

Programs

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