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}.

-1, 4, -6, 30, -18, 42, -30, -22, 128, -112, 98, 90, -78, -70, 36, 248, -232, 158, 150, -280, 182, -142, -130, 420, 210, -198, 222, -210, -1074, 1326, -238, 560, -1092, 1212, -592, 36, 350, -310, 36, 728, -1428, 1548, -378, 402, -1966, 144, 1832, 462, -450, -442

Offset: 1

Author

N. J. A. Sloane, Aug 06 2000

Keywords

• sign

Comments

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

Links

• Stefano Spezia, Table of n, a(n) for n = 1..10000
• L. Panaitopol, On the sequence p(n)^2=p(n-1)*p(n+1), J. Inequal. Pure Appl. Math., Volume 3, Issue 4, Article 53, 2002.

Crossrefs

Cf. A000040, A046868, A056222, A233671, A342567.

Programs

Maple

A056221 := proc(n)
        ithprime(n+1)^2-ithprime(n)*ithprime(n+2) ;
end proc:
seq(A056221(n),n=1..10) ; # R. J. Mathar, Dec 10 2011

Mathematica

a[n_]:=Prime[n+1]^2-Prime[n]Prime[n+2]; Array[a,50] (* Stefano Spezia, Jul 15 2024 *)

Formula

a(n) = determinant of matrix

| prime(n+1) prime(n)|

| prime(n+2) prime(n+1)|. - Zak Seidov, Jul 23 2008, indices corrected by Gary Detlefs, Dec 09 2011

a(n) = 2*A342567(n+1) for n >= 2. - Hugo Pfoertner, Jun 20 2021