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A056221 Image of primes (A000040) under "little Hankel" transform that sends [c_0, c_1, ...] to [d_0, d_1, ...] where d_n = c_n^2 - c_{n+1}*c_{n-1}.

%I A056221 #33 Jul 16 2024 15:56:07
%S A056221 -1,4,-6,30,-18,42,-30,-22,128,-112,98,90,-78,-70,36,248,-232,158,150,
%T A056221 -280,182,-142,-130,420,210,-198,222,-210,-1074,1326,-238,560,-1092,
%U A056221 1212,-592,36,350,-310,36,728,-1428,1548,-378,402,-1966,144,1832,462,-450,-442
%N A056221 Image of primes (A000040) under "little Hankel" transform that sends [c_0, c_1, ...] to [d_0, d_1, ...] where d_n = c_n^2 - c_{n+1}*c_{n-1}.
%C A056221 a(n) > 0 if and only if n+1 is in A046868. a(n) < 0 if and only if n+1 is in A233671. - _Chai Wah Wu_, Sep 10 2019
%H A056221 Stefano Spezia, <a href="/A056221/b056221.txt">Table of n, a(n) for n = 1..10000</a>
%H A056221 L. Panaitopol, <a href="http://jipam.vu.edu.au/v3n4/053_02.html">On the sequence p(n)^2=p(n-1)*p(n+1)</a>, J. Inequal. Pure Appl. Math., Volume 3, Issue 4, Article 53, 2002.
%F A056221 a(n) = determinant of matrix
%F A056221 | prime(n+1) prime(n)|
%F A056221 | prime(n+2) prime(n+1)|. - _Zak Seidov_, Jul 23 2008, indices corrected by _Gary Detlefs_, Dec 09 2011
%F A056221 a(n) = 2*A342567(n+1) for n >= 2. - _Hugo Pfoertner_, Jun 20 2021
%p A056221 A056221 := proc(n)
%p A056221         ithprime(n+1)^2-ithprime(n)*ithprime(n+2) ;
%p A056221 end proc:
%p A056221 seq(A056221(n),n=1..10) ; # _R. J. Mathar_, Dec 10 2011
%t A056221 a[n_]:=Prime[n+1]^2-Prime[n]Prime[n+2]; Array[a,50] (* _Stefano Spezia_, Jul 15 2024 *)
%Y A056221 Cf. A000040, A046868, A056222, A233671, A342567.
%K A056221 sign
%O A056221 1,2
%A A056221 _N. J. A. Sloane_, Aug 06 2000