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
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:
A341280_list.append(k)
if isprime(k):
d -= k
if isprime(k2):
d += k2
k += 1
k2 += 2 # Chai Wah Wu, Feb 16 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Feb 16 2021
EXTENSIONS
a(26)-a(31) from Chai Wah Wu, Feb 16 2021
a(32) from Chai Wah Wu, Feb 17 2021
a(33)-a(36) from Martin Ehrenstein, Feb 21 2021
STATUS
approved