The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A273785 Numbers n where a composite c < n exists such that n^(c-1) == 1 (mod c^2), i.e., such that c is a "base-n Wieferich pseudoprime". 2
17, 26, 33, 37, 49, 65, 73, 80, 81, 82, 97, 99, 101, 109, 113, 129, 145, 146, 161, 163, 168, 170, 177, 181, 182, 193, 197, 199, 201, 209, 217, 224, 225, 226, 239, 241, 242, 244, 251, 253, 257, 268, 273, 289, 293, 301, 305, 321, 323, 325, 337, 353, 360, 361 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Contains n+1 for n in A048111. - Robert Israel, Apr 20 2017
LINKS
EXAMPLE
15 satisfies the congruence 26^(15-1) == 1 (mod 15^2) and 15 < 26, so 26 is a term of the sequence.
MAPLE
N:= 1000: # to get all terms <= N
Res:= {}:
for c from 4 to N-1 do
if not isprime(c) then
for m in map(rhs@op, [msolve(x^(c-1)-1, c^2)]) do
if m > c and m <= N then Res:= Res union {m, seq(k*c^2+m, k=1..(N-m)/c^2)}
else Res:= Res union {seq(k*c^2+m, k=1..(N-m)/c^2)}
fi
od
fi
od:
sort(convert(Res, list)); # Robert Israel, Apr 20 2017
MATHEMATICA
nn = 361; c = Select[Range@ nn, CompositeQ]; Select[Range@ nn, Function[n, Count[TakeWhile[c, # <= n &], k_ /; Mod[n^(k - 1), k^2] == 1] > 0]] (* Michael De Vlieger, May 30 2016 *)
PROG
(PARI) is(n) = forcomposite(c=1, n-1, if(Mod(n, c^2)^(c-1)==1, return(1))); return(0)
CROSSREFS
Sequence in context: A129910 A259075 A212909 * A171169 A316561 A034963
KEYWORD
nonn
AUTHOR
Felix Fröhlich, May 30 2016
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 June 15 19:43 EDT 2024. Contains 373410 sequences. (Running on oeis4.)