A196202 - OEIS

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A196202

a(n) = 2^(prime(n)-1) mod prime(n)^2.

2, 4, 16, 15, 56, 40, 222, 58, 392, 30, 187, 38, 944, 1076, 2069, 1909, 473, 2197, 671, 143, 4089, 1502, 3985, 535, 5530, 9293, 6078, 1392, 7304, 9380, 2287, 2228, 7262, 4171, 14305, 8457, 12875, 10922, 7850, 520, 8951, 26789, 9551, 20073, 34476, 26866

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

OFFSET

1,1

COMMENTS

a(A049084(A001220(1))) = a(A049084(A001220(2))) = 1.

REFERENCES

N. G. W. H. Beeger, On a new case of the congruence 2^(p-1) ≡ 1 (p^2), Messenger of Mathematics 51, (1922), p. 149-150

Paulo Ribenboim, 1093 (Chap 8), in 'My Numbers, My Friends', Springer-Verlag 2000 NY, page 213ff.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

W. Meissner, Über die Teilbarkeit von 2^p-2 durch das Quadrat der Primzahl p = 1093, Sitzungsberichte Königlich Preussischen Akadamie Wissenschaften Berlin, 35 (1913), 663-667. [Annotated scanned copy]

Eric Weisstein's World of Mathematics, Wieferich Prime.

Wikipedia, Wieferich prime.

EXAMPLE

A001220(1)=1093=A000040(183): a(183)=1, or a(A049084(A001220(1)))=1;

A001220(2)=3511=A000040(490): a(490)=1, or a(A049084(A001220(2)))=1.

MAPLE

seq(2 &^ (ithprime(n)-1) mod ithprime(n)^2, n=1..1000); # Robert Israel, Aug 03 2014

MATHEMATICA

PowerMod[2, #-1, #^2]&/@Prime[Range[50]] (* Harvey P. Dale, Apr 25 2012 *)

PROG

(PARI) forprime(p=2, 1e2, print1(lift(Mod(2, p^2)^(p-1)), ", ")) \\ Felix Fröhlich, Aug 03 2014

(Haskell)