

A105016


Smallest a(n) such that a(n)^2  n is a positive prime, or 0 if no such a(n) exists.


2



0, 2, 2, 4, 3, 4, 3, 3, 5, 4, 9, 4, 5, 4, 4, 14, 0, 6, 5, 6, 5, 8, 5, 5, 11, 6, 7, 8, 9, 6, 7, 6, 7, 6, 6, 8, 7, 12, 7, 10, 9, 8, 7, 12, 7, 8, 7, 7, 11, 0, 9, 8, 9, 8, 11, 12, 13, 8, 9, 8, 11, 8, 8, 10, 9, 12, 13, 18, 9, 10, 9, 10, 13, 12, 9, 16, 9, 10, 9, 9, 11, 10, 21, 10, 11, 12, 13, 10, 15, 10
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


REFERENCES

An old ARML problem asked for the smallest n>0 such that a(n) does not exist.


LINKS

T. D. Noe, Table of n, a(n) for n = 0..10000


EXAMPLE

a(8) = 5 because 5^2  8 = 17 is the smallest square that gives a prime difference.
a(16) = 0 because if x^2  16 is prime, then a prime equals (x+4)(x4), which is impossible.


MATHEMATICA

Table[s = Sqrt[n]; If[IntegerQ[s], If[PrimeQ[(s + 1)^2  n], k = s + 1, k = 0], k = Ceiling[s]; While[! PrimeQ[k^2  n], k++]]; k, {n, 0, 100}] (* T. D. Noe, Apr 17 2011 *)


CROSSREFS

Cf. A075555 for the primes = a(n)^2  n.
Sequence in context: A209138 A051297 A078317 * A074747 A128248 A224901
Adjacent sequences: A105013 A105014 A105015 * A105017 A105018 A105019


KEYWORD

nonn


AUTHOR

Joshua Zucker, Mar 31 2005


STATUS

approved



