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

1,4

Comments

a(n) is the 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 exist 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, b-1], _?(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