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A257545 a(0) = 2, a(n) = smallest prime p such that none of p - 1, p - 2,... p - n are squarefree. 2
2, 5, 29, 101, 5051, 5051, 73453, 671353, 130179187, 211014929, 262315477, 3639720053 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..11.

FORMULA

a(n) << A002110(n)^10 by the CRT and Xylouris' improvement to Linnik's theorem. - Charles R Greathouse IV, Apr 29 2015

EXAMPLE

a(3) = 101 because 101 is prime and none of 101 - 1 = 100, 101 - 2 = 99, and 101 - 3 = 98 are squarefree.

MAPLE

p:= 2:

A[0]:= 2:

m:= 0:

while p < 10^6 do

p:= nextprime(p);

for k from 1 while not numtheory:-issqrfree(p-k) do od:

if k > m+1 then

   for j from m+1 to k-1 do A[j]:= p od:

   m:= k-1;

fi

od:

seq(A[i], i=0..m); # Robert Israel, Apr 29 2015

PROG

(PARI) a(n)=forprime(p=2, , for(k=1, n, if(issquarefree(p-k), next(2))); return(p)) \\ Charles R Greathouse IV, Apr 29 2015

CROSSREFS

Cf. A257108.

Sequence in context: A083472 A213996 A057794 * A073715 A104083 A257163

Adjacent sequences:  A257542 A257543 A257544 * A257546 A257547 A257548

KEYWORD

nonn,more

AUTHOR

Juri-Stepan Gerasimov, Apr 29 2015

EXTENSIONS

a(9)-a(11) from Charles R Greathouse IV, Apr 29 2015

STATUS

approved

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Last modified January 27 03:09 EST 2022. Contains 350601 sequences. (Running on oeis4.)