A323701 a(n) is the number of primes p such that A007504(n) <= p < A007504(n+1).

2, 2, 2, 3, 3, 4, 5, 4, 6, 6, 7, 7, 8, 7, 9, 10, 10, 8, 12, 12, 11, 12, 12, 15, 14, 14, 14, 14, 17, 17, 16, 17, 19, 19, 22, 16, 24, 21, 20, 20, 20, 28, 22, 26, 21, 24, 28, 23, 31, 23, 30, 28, 28, 32, 28, 31, 30, 27, 35, 30, 32, 31, 38, 34, 38, 36, 36, 37, 35, 35

Offset: 1

Author

David James Sycamore, Jan 24 2019

Keywords

• nonn

Comments

Corresponds to the number of terms in A321578 which are equal to n.

Examples

			a(1)=2 because 2 <= 2, 3 < 5;
a(5)=3 because 28 <= 29, 31, 37 < 41.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A007504, A321578, A061568.

Programs

Mathematica

nn = 1375; MapIndexed[Set[s[First[#2]], #1] &, Accumulate[Prime@ Range[nn]]]; c = 0; j = k = 1; Rest@ Reap[Do[p = Prime[n]; While[s[k] <= p, k++]; If[j == k, c++, Sow[c + 1]; c = 0]; j = k, {n, nn}] ][[-1, 1]] (* Michael De Vlieger, Jun 29 2025 *)

Perl

use ntheory ':all'; sub a { my $p = nth_prime($[0]+1); my $s = sum_primes($p); prime_count($s-$p, $s-1) }; print join(", ", map { a($) } 1..100), "\n"; # Daniel Suteu, Jan 25 2019

Extensions

More terms from Daniel Suteu, Jan 25 2019