|
|
A341280
|
|
Numbers k such that A073837(k) is a multiple of k.
|
|
2
|
|
|
1, 4, 6, 8, 10, 12, 17, 20, 31, 34, 52, 85, 92, 555, 1723, 2870, 2904, 3943, 19325, 41708, 145474, 225476, 240632, 666862, 8911645, 10249751, 138543006, 209659550, 265831784, 540388470, 949428097, 2813155218, 12323589092, 407224380494, 1704233306223, 3361207818001
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Numbers k such that the sum of primes from k to 2*k is divisible by k.
Primes in the sequence include 17, 31, 1723, 3943.
Conjecture: For n > 1, a(n) is prime if and only if a(n) is odd and not a multiple of 5. - Chai Wah Wu, Feb 17 2021
The conjecture is false because a(35) = 1704233306223 is divisible by 3 and a(36) = 3361207818001 is divisible by 11. - Martin Ehrenstein, Feb 21 2021
|
|
LINKS
|
|
|
EXAMPLE
|
a(3) = 6 is a term because A073837(6) = 7+11 = 18 is divisible by 6.
|
|
MAPLE
|
R:= 1: S:= [2, 3]: s:= 5: q:= 5: count:= 1:
for n from 3 while count < 24 do
if n = S[1]+1 then S:= S[2..-1]; s:= s-n+1 fi;
if q <= 2*n then S:= [op(S), q]; s:= s+q; q:= nextprime(q) fi;
if s mod n = 0 then count:= count+1; R:= R, n fi;
od:
R;
|
|
PROG
|
(Python)
from sympy import isprime
k, k2, d, A341280_list = 1, 3, 2, []
while k < 10**10:
if d % k == 0:
if isprime(k):
d -= k
if isprime(k2):
d += k2
k += 1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|