|
|
|
|
2, 9, 15, 28, 40, 41, 42, 48, 60, 68, 79, 83, 93, 95, 98, 100, 108, 114, 118, 120, 124, 129, 132, 137, 147, 149, 167, 196, 202, 206, 207, 215, 219, 221, 223, 225, 230, 243, 248, 255, 261, 265, 274, 276, 287, 299, 302, 320, 323, 329, 337, 341, 353, 356, 360, 364, 365, 373, 380, 381, 391, 405, 410
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Numbers k such that A125611(k)^6 - 1 is divisible by 7^(k+1).
|
|
LINKS
|
|
|
EXAMPLE
|
a(3) = 15 is a term because A125611(15) = a125611(16) = 56020344873707, i.e., 56020344873707 is the least prime p such that p^6 - 1 is divisible by 7^15, and in this case p^6 - 1 is also divisible by 7^16.
|
|
MAPLE
|
f:= proc(n) local R, r, i;
R:= sort(map(rhs@op, [msolve(x^6=1, 7^n)]));
for i from 0 do
for r in R do
if isprime(7^n * i + r) then return 7^n * i + r fi
od od;
end proc:
R:= NULL: count:= 0:
for k from 1 while count < 100 do
v:= f(k);
if v = w then R:= R, k-1; count:= count+1 fi;
w:= v;
od:
R;
|
|
PROG
|
(Python)
from itertools import count, islice
from sympy import nthroot_mod, isprime
def A369154_gen(): # generator of terms
c, m = 1, 1
for k in count(0):
m *= 7
r = sorted(nthroot_mod(1, 6, m, all_roots=True))
for i in count(0, m):
for p in r:
if isprime(i+p):
if i+p == c:
yield k
c = i+p
break
else:
continue
break
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|