

A206400


Number of composites of the form n^2 + 1 between two successive primes of this form.


6



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
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OFFSET

1,4


COMMENTS

a(n) = number of composites of A134406 between A002496(n) and A002496(n+1).


LINKS

Michel Lagneau, Table of n, a(n) for n = 1..10000


EXAMPLE

a(4) = 3 because there exists 3 composite numbers of the form n^2+1 : {50, 65, 82} between A002496(4) = 37 and A002496(5) = 101.


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:


MATHEMATICA

cfn2[{a_, b_}]:=Count[Range[a+1, b1], _?(IntegerQ[Sqrt[#1]]&)]; cfn2/@ Partition[ Select[Prime[Range[50000]], IntegerQ[Sqrt[#1]]&], 2, 1] (* Harvey P. Dale, Jan 13 2019 *)


PROG

(PARI) c=0; for(n=2, 1e9, !ispseudoprime(n^2+1) & c++ & next; print1(c", "); c=0) \\ M. F. Hasler, Feb 07 2012


CROSSREFS

Cf. A002522, A002496, A134406.
Sequence in context: A220670 A264526 A138071 * A321129 A278265 A171369
Adjacent sequences: A206397 A206398 A206399 * A206401 A206402 A206403


KEYWORD

nonn


AUTHOR

Michel Lagneau, Feb 07 2012


STATUS

approved



