A376754 Length of n-th run of primes in A376198.

2, 3, 4, 8, 13, 24, 43, 78, 142, 261, 479, 894, 1674, 3118, 5873, 11102, 20992, 39830, 75906, 144652, 276720, 529865, 1016535, 1954167, 3761091, 7250277, 13993031, 27042169, 52313384, 101320082, 196422988, 381154209, 740280217, 1438969498, 2799310690, 5449726356

Offset: 1

Author

N. J. A. Sloane, Oct 03 2024

Keywords

• nonn

Comments

Theorem: a(n) is the number of steps needed for the prime A376751(n) to "double" in the normal sequence of primes. More precisely, if A376751(n) = prime(j), then a(n) = A063124(j). For example, A376751(8) = 521 = prime(98), and A063124(98) = 78 = a(8). (The result seems to be off by 1 at n = 4, for reasons I don't understand yet.) - N. J. A. Sloane, Oct 04 2024

Crossrefs

Cf. A376198-A376201, A376750-A376753.

See also A063124.

Programs

Python

# uses code in A376750
print([out[4] for out in list(islice(A376750_4gen(), 15))]) # Michael S. Branicky, Oct 03 2024

Extensions

a(14)-a(33) from Michael S. Branicky, Oct 04 2024

a(34)-a(36) from Michael S. Branicky, Oct 07 2024