login
A366941
a(n) is the least k such that k == 1 (mod 6) and k has exactly n prime factors, counted with multiplicity.
0
7, 25, 175, 625, 4375, 15625, 109375, 390625, 2734375, 9765625, 68359375, 244140625, 1708984375, 6103515625, 42724609375, 152587890625, 1068115234375, 3814697265625, 26702880859375, 95367431640625, 667572021484375, 2384185791015625, 16689300537109375, 59604644775390625, 417232513427734375, 1490116119384765625
OFFSET
1,1
FORMULA
a(n) = 5^n if n is even,
5^(n-1) * 7 if n is odd.
a(n + 2) = 25 * a(n).
G.f.: z * (7 + 25 * z)/(1 - 25 * z^2).
From Amiram Eldar, Nov 10 2023: (Start)
Sum_{n>=1} 1/a(n) = 4/21.
Sum_{n>=1} (-1)^(n+1)/a(n) = 3/28. (End)
EXAMPLE
a(3) = 175 because 175 == 1 (mod 6) and 175 = 5^2 * 7 has 3 prime factors, counted with multiplicity.
MAPLE
f:= proc(n) if n::odd then 7 * 5^(n-1) else 5^n fi end proc:
map(f, [$1..30]);
MATHEMATICA
LinearRecurrence[{0, 25}, {7, 25}, 26] (* Amiram Eldar, Nov 10 2023 *)
CROSSREFS
Sequence in context: A151491 A208425 A334651 * A191237 A088009 A293532
KEYWORD
nonn,easy
AUTHOR
Zak Seidov and Robert Israel, Oct 31 2023
STATUS
approved