A206786 Remainder of n^340 divided by 341.

1, 1, 56, 1, 67, 56, 56, 1, 67, 67, 253, 56, 67, 56, 1, 1, 56, 67, 56, 67, 67, 253, 1, 56, 56, 67, 1, 56, 1, 1, 155, 1, 187, 56, 1, 67, 56, 56, 1, 67, 67, 67, 56, 253, 56, 1, 1, 56, 67, 56, 67, 67, 67, 1, 242, 56, 67, 1, 56, 1, 1, 155, 1, 1, 56, 187, 67

Offset: 1

Author

Alonso del Arte, Feb 12 2012

Keywords

• nonn
• easy

Comments

The n for which a(n) = 1 indicate the bases to which 341 is a Fermat pseudoprime. 341 is the smallest base 2 Fermat pseudoprime.

The only a(n) that occur are 0, 1, 56, 67, 155, 187, 242, 253. If n is one of these eight numbers, then a(n) = n.

Periodic with period 341. - Charles R Greathouse IV, May 01 2012

Examples

			a(2) = 1 because 2^340/341 leaves a remainder of 1 (the prime factors of 2^340 - 1 include 11 and 31).
a(3) = 56 because 3^340/341 leaves a remainder of 56 (the prime factors of 3^340 - 56 are 5, 11, 31 and a prime number with more than a hundred digits).
		

References

• David Wells, Prime Numbers: The Most Mysterious Figures in Math. Hoboken, New Jersey: John Wiley & Sons (2005): 191

Links

• Index entries for linear recurrences with constant coefficients, order 341.

Crossrefs

Cf. A200146, A066340, A230579.

Programs

Mathematica

Table[Mod[n^340, 341], {n, 100}]
PowerMod[Range[80],340,341] (* Harvey P. Dale, Jun 04 2017 *)

PARI

a(n)=lift(Mod(n,341)^340) \\ Charles R Greathouse IV, May 01 2012