A106546 -id:A106546 - cp's OEIS frontend

A106564 Perfect squares which are not the difference of two primes.

25, 49, 121, 169, 289, 361, 529, 625, 729, 841, 961, 1225, 1369, 1681, 1849, 2209, 2401, 2601, 2809, 3025, 3481, 3721, 3969, 4225, 4489, 4761, 5041, 5329, 5625, 5929, 6241, 6889, 7225, 7569, 7921, 8281, 8649, 9025, 9409, 10201, 10609, 11449, 11881

Offset: 1

Alexandre Wajnberg, May 09 2005

Squares in A269345; see also the Mathematica code. - Waldemar Puszkarz, Feb 27 2016

It is conjectured (see A020483) that every even number is a difference of primes, and this is known to be true for even numbers < 10^11. If so,this sequence consists of the odd squares n such that n+2 is composite. - Robert Israel, Feb 28 2016

			a(2)=49 because it is the second perfect square which is impossible to obtain subtracting a prime from another one.
64 is not in the sequence because 64=67-3 (difference of two primes).

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A020483, A106544-A106548, A106562-A106563, A106571, A106573-A106575, A106577.

[n^2: n in [1..150]| not IsPrime(n^2+2) and n mod 2 eq 1]; // Vincenzo Librandi, Feb 28 2016

remove(t -> isprime(t+2), [seq(i^2, i=1..1000, 2)]); # Robert Israel, Feb 28 2016

With[{lst=Union[(#[[2]]-#[[1]])&/@Subsets[Prime[Range[2000]], {2}]]}, Select[Range[140]^2, !MemberQ[lst,#]&]] (* Harvey P. Dale, Jan 04 2011 *)
Select[Range[1,174,2]^2, !PrimeQ[#+2]&]
Select[Select[Range[30000], OddQ[#]&& !PrimeQ[#]&& !PrimeQ[#+2]&], IntegerQ[Sqrt[#]]&] (* Waldemar Puszkarz, Feb 27 2016 *)

for(n=1, 174, n%2==1&&!isprime(n^2+2)&&print1(n^2, ", ")) \\ Waldemar Puszkarz, Feb 27 2016

n^2 - A106546 with 0's removed.

Extended by Ray Chandler, May 12 2005

A106548 Perfect squares n^2 which are both the sum and the difference of two primes (otherwise 0).

Original entry on oeis.org

0, 4, 9, 16, 0, 36, 0, 64, 81, 100, 0, 144, 0, 196, 225, 256, 0, 324, 0, 400, 441, 484, 0, 576, 0, 676, 0, 784, 0, 900, 0, 1024, 1089, 1156, 0, 1296, 0, 1444, 0, 1600, 0, 1764, 0, 1936, 0, 2116, 0, 2304, 0, 2500, 0, 2704, 0, 2916, 0, 3136, 0, 3364, 0, 3600, 0, 3844, 0

Offset: 1

Alexandre Wajnberg, May 08 2005

Cf. A106544-A106547, A106562-A106564, A106571, A106573-A106575, A106577.

a(n) = Min(A106545(n), A106546(n)).

Extended by Ray Chandler, May 12 2005

A106547 Perfect squares n^2 which are neither the sum nor the difference of two primes (otherwise 0).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 121, 0, 0, 0, 0, 0, 289, 0, 0, 0, 0, 0, 529, 0, 625, 0, 0, 0, 0, 0, 961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1681, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2601, 0, 2809, 0, 0, 0, 0, 0, 3481, 0, 0, 0, 0, 0, 4225, 0, 4489, 0, 0, 0, 0, 0, 5329, 0, 0, 0, 0, 0, 6241, 0, 0, 0, 6889, 0

Offset: 1

Alexandre Wajnberg, May 08 2005

Cf. A106544-A106548, A106562-A106564, A106571, A106573-A106575, A106577.

a(n) = Min(A106544(n), n^2-A106546(n)).

Corrected and extended by Ray Chandler, May 12 2005

A108321 a(n) = n^2 if n^2 is not the difference of two primes; otherwise a(n) = 0.

Original entry on oeis.org

0, 0, 0, 0, 25, 0, 49, 0, 0, 0, 121, 0, 169, 0, 0, 0, 289, 0, 361, 0, 0, 0, 529, 0, 625, 0, 729, 0, 841, 0, 961, 0, 0, 0, 1225, 0, 1369, 0, 0, 0, 1681, 0, 1849

Offset: 0

Alexandre Wajnberg, Jun 30 2005

This sequence is also n^2 - A106546

			a(4)=0 because the fourth perfect square 16 is the difference between two primes: 19-3. a(5)=25 figures here because the nearest prime greater than 25 is 29 and the difference 29-25 is 4 (an even number >2), thus not a prime; all other greater primes are odd and the difference with 25 will give an even number, thus again not a prime.

Cf. A106546, A106564, A098108, A106571.

cp's OEIS Frontend

A106564 Perfect squares which are not the difference of two primes.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

Extensions

A106548 Perfect squares n^2 which are both the sum and the difference of two primes (otherwise 0).

Views

Author

Keywords

Crossrefs

Formula

Extensions

A106547 Perfect squares n^2 which are neither the sum nor the difference of two primes (otherwise 0).

Views

Author

Keywords

Crossrefs

Formula

Extensions

A108321 a(n) = n^2 if n^2 is not the difference of two primes; otherwise a(n) = 0.

Views

Author

Keywords

Comments

Examples

Crossrefs