A206400 Number of composites of the form n^2 + 1 between two successive primes of this form.
0, 1, 1, 3, 3, 1, 3, 3, 1, 9, 3, 13, 1, 9, 7, 9, 5, 3, 15, 5, 3, 3, 1, 3, 3, 11, 3, 5, 3, 9, 5, 3, 3, 19, 1, 3, 13, 5, 5, 3, 9, 5, 3, 3, 5, 9, 3, 15, 5, 7, 11, 13, 9, 33, 1, 9, 3, 5, 13, 9, 5, 3, 3, 19, 1, 3, 3, 15, 5, 39, 7, 11, 13, 5, 7, 9, 39, 1, 7, 1, 7
Offset: 1
Keywords
Examples
a(4) = 3 because there exist 3 composite numbers of the form n^2+1 : {50, 65, 82} between A002496(4) = 37 and A002496(5) = 101.
Links
- Michel Lagneau, Table of n, a(n) for n = 1..10000
Programs
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Maple
i:=0:for n from 2 to 1000 do:x:=n^2+1:if type (x,prime)=true then printf(`%d, `,i):i:=0:else i:=i+1:fi:od:
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Mathematica
cfn2[{a_,b_}]:=Count[Range[a+1,b-1],?(IntegerQ[Sqrt[#-1]]&)]; cfn2/@ Partition[ Select[Prime[Range[50000]],IntegerQ[Sqrt[#-1]]&],2,1] (* _Harvey P. Dale, Jan 13 2019 *) -
PARI
c=0; for(n=2,1e9, !ispseudoprime(n^2+1) & c++ & next; print1(c","); c=0) \\ M. F. Hasler, Feb 07 2012
Comments