login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A258045 Table T(b, m) of largest exponents k such that for p = prime(m) and base b > 1 the congruence b^(p-1) == 1 (mod p^k) is satisfied, or 0 if no such k exists, read by antidiagonals (downwards). 3
0, 1, 1, 1, 0, 0, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 2, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 0, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,10

COMMENTS

Table starts

b=2:  0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...

b=3:  1, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...

b=4:  0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...

b=5:  2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...

b=6:  0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...

b=7:  1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...

b=8:  0, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...

b=9:  3, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...

b=10: 0, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...

b=11: 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...

b=12: 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...

b=13: 2, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 ...

b=14: 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1 ...

b=15: 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...

b=16: 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...

b=17: 4, 2, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1 ...

b=18: 0, 0, 2, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1 ...

b=19: 1, 2, 1, 3, 1, 2, 1, 0, 1, 1, 1, 1, 1, 2 ...

b=20: 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...

....

a(n) > 1 if b appears in row k, column n of the table in A257833 for k > 1 and n > 1.

LINKS

Table of n, a(n) for n=2..88.

FORMULA

a(n, m) = T(m+1, n-m), n >=2, m = 1, 2, ..., n-1. - Wolfdieter Lang, Jun 29 2015

EXAMPLE

T(3, 5) = 2, because the largest Wieferich exponent of prime(5) = 11 in base 3 is 2.

The triangle a(n ,m) begins:

  m 1 2 3 4 5 6 7 8 9 10 11 ...

n

2   0

3   1 1

4   1 0 0

5   1 1 1 2

6   1 1 1 1 0

7   1 2 1 0 0 1

8   1 1 1 1 1 1 0

9   1 1 1 1 1 2 2 3

10  1 1 1 1 1 0 1 0 0

11  1 1 1 1 1 1 1 1 2  1

12  1 1 1 1 1 1 1 1 0  1  0

...

PROG

(PARI) for(b=2, 20, forprime(p=1, 70, k=0; while(Mod(b, p^k)^(p-1)==1, k++); if(k > 0, k--); print1(k, ", ")); print(""))

CROSSREFS

Cf. A001220, A257833.

Sequence in context: A037818 A087116 A033264 * A239302 A256983 A330720

Adjacent sequences:  A258042 A258043 A258044 * A258046 A258047 A258048

KEYWORD

nonn,tabl

AUTHOR

Felix Fröhlich, May 26 2015

EXTENSIONS

Edited. - Wolfdieter Lang, Jun 29 2015

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 19 13:56 EDT 2020. Contains 337178 sequences. (Running on oeis4.)