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A349767
Numbers m such that 2^m - m is divisible by 5.
3
3, 14, 16, 17, 23, 34, 36, 37, 43, 54, 56, 57, 63, 74, 76, 77, 83, 94, 96, 97, 103, 114, 116, 117, 123, 134, 136, 137, 143, 154, 156, 157, 163, 174, 176, 177, 183, 194, 196, 197, 203, 214, 216, 217, 223, 234, 236, 237, 243, 254, 256, 257, 263, 274, 276, 277, 283, 294, 296, 297, 303
OFFSET
1,1
COMMENTS
For every prime p, there are infinitely many numbers m such that 2^m - m (A000325) is divisible by p, here are numbers m corresponding to p = 5.
Equivalently, numbers that are congruent to {3, 14, 16, 17, 23, 34, 36, 37, 43, 54, 56, 57} mod 60, <==> numbers that are congruent to {+-3, +-14, +-16, +-17, +-23, +-34} mod 60.
REFERENCES
Michael Doob, The Canadian Mathematical Olympiad & L'Olympiade Mathématique du Canada 1969-1993, Canadian Mathematical Society & Société Mathématique du Canada, Problem 4, 1983, page 158, 1993.
LINKS
The IMO Compendium, Problem 4, 15th Canadian Mathematical Olympiad 1983.
MAPLE
filter:= n -> 2^n-n mod 5 = 0 : select(filter, [$1..400]);
MATHEMATICA
Select[Range[300], PowerMod[2, #, 5] == Mod[#, 5] &] (* Amiram Eldar, Dec 10 2021 *)
PROG
(PARI) isok(m) = Mod(2, 5)^m == Mod(m, 5); \\ Michel Marcus, Dec 10 2021
(Python)
def ok(n): return pow(2, n, 5) == n%5
print([k for k in range(357) if ok(k)]) # Michael S. Branicky, Dec 10 2021
CROSSREFS
Similar with: A299174 (p = 2), A047257 (p = 3), this sequence (p = 5).
Sequence in context: A016062 A009401 A195864 * A022890 A032920 A134767
KEYWORD
nonn
AUTHOR
Bernard Schott, Dec 10 2021
STATUS
approved