A321578 a(n) is the maximum value of k such that A007504(k) <= prime(n).

1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15

Offset

1,3

Comments

Let A be A007504. The number of distinct values of k such that a(k)=r is the number of primes p in the interval A(r) <= p < A(r+1); namely: 2,2,2,3,3,4,5,4,6,6,... (see A323701). Let b(n) be the smallest r such that a(r)=n, namely: 1,3,5,7,10,13,17,22,26,... For given n, if k is the index of the smallest prime >= A(n), then b(n)=k. (The equality applies when n is a term of A013916.)

Links

Table of n, a(n) for n=1..74.

Example

a(1)=1 since prime(1)=2 and 1 is max k such that A007504(k) <= 2.
a(5)=3 since prime(5)=11 and 3 is max k such that A007504(k) <= 11.
n=4 (in A013916). A(4)=17=prime(7), so b(4)=7.
n=7 (not in A013916). A(7)=58 < 59=prime(17), so b(7)=17.

Prog

(Perl) use ntheory ':all'; sub a { my $p = nth_prime($_[0]); my($s, $q) = (0, 2); while ($s <= $p) { $s += $q; $q = next_prime($q) }; prime_count($q-1)-1 }; print join(", ", map { a($_) } 1..100), "\n"; # Daniel Suteu, Jan 26 2019
(PARI) a(n) = my(k=0, p=0, s=0); while(s <= prime(n), k++; p=nextprime(p+1); s+=p); k-1; \\ Michel Marcus, Feb 19 2019

Crossrefs

Cf. A000040, A007504, A013916, A323701, A061568.

Sequence in context: A126848 A232753 A067085 * A055086 A001462 A357021

Adjacent sequences: A321575 A321576 A321577 * A321579 A321580 A321581

Keyword

nonn

Author

David James Sycamore, Nov 12 2018

Status

approved