A391805 a(n) = greatest prime less than prime(n)*prime(n+1).

5, 13, 31, 73, 139, 211, 317, 433, 661, 887, 1129, 1511, 1759, 2017, 2477, 3121, 3593, 4079, 4751, 5179, 5749, 6553, 7369, 8629, 9791, 10399, 11003, 11657, 12301, 14347, 16633, 17939, 19037, 20707, 22483, 23689, 25589, 27211, 28879, 30949, 32381, 34549

Offset

1,1

Comments

Conjecture: If k is an even integer greater than 4, then A391804(n) - a(n) = k for infinitely many n.

Links

Table of n, a(n) for n=1..42.

Example

5 is the greatest prime less than 2*3, so a(1) = 5.

Maple

seq(prevprime(ithprime(k)*ithprime(k+1)), k=1..100); # Robert Israel, Jan 05 2026

Mathematica

Table[NextPrime[Prime[n]*Prime[n + 1], -1], {n, 1, 50}]

Crossrefs

Cf. A000040, A006094, A391804.

Sequence in context: A118646 A097969 A082280 * A007708 A146609 A121129

Adjacent sequences: A391802 A391803 A391804 * A391806 A391807 A391808

Keyword

nonn,easy

Author

Clark Kimberling, Jan 04 2026

Status

approved