A079636 Smallest number whose reciprocal fits in the square-root gap of consecutive primes.

4, 2, 3, 2, 4, 2, 5, 3, 2, 6, 2, 4, 7, 4, 3, 3, 8, 3, 5, 9, 3, 5, 4, 3, 5, 11, 6, 11, 6, 2, 6, 4, 12, 3, 13, 5, 5, 7, 5, 5, 14, 3, 14, 7, 15, 3, 3, 8, 16, 8, 6, 16, 4, 6, 6, 6, 17, 6, 9, 17, 4, 3, 9, 18, 9, 3, 7, 4, 19, 10, 7, 5, 7, 7, 10, 7, 5, 10, 6, 5, 21

Offset

1,1

Comments

Is the limit of sqrt(P_(n+1)) - sqrt(P_n) = 0?

References

Jim Ferry, sci.math, Jan 30 2003

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Formula

a(n) = ceiling(1/(w'-w)) where w=sqrt(p(n)) and w'=sqrt(p(n+1)).

a(n) = A252477(n) + 1. - Hugo Pfoertner, Aug 23 2025

Example

a(3) = 3 because p(3)=5, p(4)=7, w=sqrt(5), w'=sqrt(7) and 1/(w'-w)=2.44.

Maple

a:= n-> ((w, v)-> ceil(1/(w-v)))(map(sqrt@ithprime, [n+1, n])[]):
seq(a(n), n=1..81);  # Alois P. Heinz, Aug 23 2025

Mathematica

Ceiling[1/Subtract @@@ Reverse[Partition[Sqrt[Prime[Range[100]]], 2, 1], 2]] (* Paolo Xausa, Aug 24 2025 *)

Crossrefs

Cf. A000040, A252477.

Sequence in context: A217435 A238352 A291357 * A308261 A019614 A051528

Adjacent sequences: A079633 A079634 A079635 * A079637 A079638 A079639

Keyword

easy,nonn

Author

Rainer Rosenthal, Jan 30 2003

Extensions

More terms from Sean A. Irvine, Aug 23 2025

Status

approved