A342839 Numbers k such that there are more primes in the interval [4*k+1, 5*k] than there are in the interval [3*k+1, 4*k].

1, 4, 7, 9, 10, 15, 16, 22, 23, 24, 25, 34, 36, 37, 39, 40, 47, 55, 56, 57, 58, 64, 67, 82, 84, 86, 87, 88, 91, 93, 94, 95, 96, 97, 98, 99, 100, 102, 104, 105, 106, 107, 130, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 144, 146, 147, 148, 149, 150, 153

Offset: 1

Author

Jon E. Schoenfield, Mar 23 2021

Keywords

• nonn

Comments

After a(876) = 11895, there are no more terms < 100000.

Conjecture: a(876) = 11895 is the final term.

There exist eight terms k for which A342068(k) != 5: A342068(k) = 2 for k = 1; A342068(k) = 3 for k = 47, 67, 95, and 1323; and A342068(k)=4 for k = 22, 57, and 102.

Examples

			The intervals [1, 100], [101, 200], [201, 300], [301, 400], and [401, 500] contain 25, 21, 16, 16, and 17 primes, respectively (cf. A038822); 17 > 16, so 100 is a term of the sequence.
		

Crossrefs

Cf. A342068, A342069, A342070, A342071.