A342071 Numbers k such that there are more primes in the interval [3*k+1, 4*k] than there are in the interval [2*k+1, 3*k].

12, 19, 22, 32, 42, 45, 49, 50, 52, 54, 57, 59, 70, 71, 72, 73, 74, 75, 101, 102, 115, 116, 117, 121, 122, 123, 124, 126, 132, 143, 180, 182, 184, 185, 186, 187, 188, 189, 190, 192, 194, 195, 197, 268, 269, 309, 310, 311, 312, 322, 323, 325, 326, 327, 328, 329

Offset: 1

Author

Jon E. Schoenfield, Mar 23 2021

Keywords

• nonn

Comments

After a(194)=3977, there are no more terms < 100000.

Conjecture: a(194)=3977 is the final term.

For each of the first 194 terms k, there are at least as many primes in [1, k] as there are in [k+1, 2*k], and at least as many primes in [k+1, 2*k] as there are in [2*k+1, 3*k], so A342068(k)=4.

Examples

			The intervals [1, 100], [101, 200], [201, 300], and [301, 400] contain 25, 21, 16, and 16 primes respectively (cf. A038822); the 4th interval does not contain more primes than does the 3rd, so 100 is not a term of the sequence.
However, the intervals [1, 101], [102, 202], [203, 303], and [304, 404] contain 26, 20, 16, and 17 primes, respectively; 17 > 16, so 101 is a term.
		

Crossrefs

Cf. A342068, A342069, A342070, A342839.