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URL: https://oeis.org/A079636

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A079636
Smallest number whose reciprocal fits in the square-root gap of consecutive primes.
2
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
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
Sequence in context: A217435 A238352 A291357 * A308261 A019614 A051528
KEYWORD
easy,nonn
AUTHOR
Rainer Rosenthal, Jan 30 2003
EXTENSIONS
More terms from Sean A. Irvine, Aug 23 2025
STATUS
approved