OFFSET
1,2
COMMENTS
Numbers k such that A058078(k)=1.
If prime(k+1)-prime(k)=2 and prime(k+2)-prime(k+1)=4, then k is in the sequence unless prime(k) == 3 (mod 8) or prime(k) == 5 (mod 9).
If prime(k+1)-prime(k)=4 and prime(k+2)-prime(k+1)=2, then k is in the sequence unless prime(k) == 7 (mod 8) or prime(k) == 7 (mod 9).
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
a(3)=6 is in the sequence because the 6th, 7th and 8th primes are 13, 17 and 19, and binomial(17,13)=2380 and binomial(19,17)=171 are coprime.
MAPLE
filter:= n -> igcd(binomial(ithprime(n+2), ithprime(n+1)), binomial(ithprime(n+1), ithprime(n)))=1:
select(filter, [$1..1000]);
PROG
(PARI) isok(k) = gcd(binomial(prime(k+2), prime(k+1)), binomial(prime(k+1), prime(k))) == 1; \\ Michel Marcus, Jul 02 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel, May 15 2020
STATUS
approved