OFFSET
1,1
COMMENTS
Such k is an even squarefree number.
Conjecture: the sequence is infinite.
EXAMPLE
a(2) = 6 because k = 2*3 = 6 is the smallest number with 2 prime factors such that 2 + 6/2 = 3 + 6/3 = 5 is prime.
From Michael De Vlieger, Nov 13 2017: (Start)
First differences of prime indices of a(n):
n a(n) A287352(a(n))
----------------------------------------------------------
1 2 1
2 6 1, 1
3 30 1, 1, 1,
4 210 1, 1, 1, 1
5 15810 1, 1, 1, 4, 4
6 292110 1, 1, 1, 1, 2, 22
7 16893030 1, 1, 1, 1, 1, 15, 7
8 984016110 1, 1, 1, 1, 1, 5, 2, 66
9 17088913842 1, 1, 2, 1, 1, 1, 1, 1, 67
10 2446241358990 1, 1, 1, 2, 1, 2, 2, 3, 1, 93
11 1098013758964122 1, 1, 2, 1, 1, 3, 2, 8, 3, 22, 10
(End)
PROG
(PARI) isok(k, n) = {if (!issquarefree(k), return (0)); if (omega(k) != n, return (0)); fordiv(k, d, if (isprime(d) && !isprime(d+k/d), return(0)); ); return (1); }
a(n) = {my(k=1); while( !isok(k, n), k++); k; } \\ Michel Marcus, Nov 11 2017
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Thomas Ordowski, Nov 11 2017
EXTENSIONS
a(5)-a(7) from Michel Marcus, Nov 11 2017
a(8) from Michel Marcus, Nov 12 2017
a(9)-a(10) from Michael De Vlieger, Nov 13 2017
a(11) (and update of table in Example section) from Jon E. Schoenfield, Nov 19 2017
STATUS
approved