A108943 -id:A108943 - cp's OEIS frontend

A108944 Minimal square k^2 such that sum of the n-th twin prime pair plus k^2 is a square.

1, 4, 1, 0, 4, 16, 1, 0, 196, 9, 400, 100, 1, 16, 4, 169, 4, 36, 1936, 1, 529, 1, 36, 100, 400, 16, 25, 10000, 10816, 49, 144, 17956, 25, 400, 0, 169, 961, 16, 2500, 25, 0, 676, 3844, 784, 100, 64, 169, 121, 400, 49, 3025, 9, 17689, 78400, 400, 20449, 100, 96100, 361

Offset: 1

Giovanni Teofilatto, Jul 21 2005

nonn

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

Cf. A001359, A006512, A033677, A040040, A108943, A108945.

P:= select(isprime,{seq(i,i=3..10^4,2)}):
TA:= sort((convert((P intersect (P +~ 2)),list) -~ 1)/~ 2):
f:= proc(m) local d;
  for d in sort(convert(numtheory:-divisors(m),list)) do
    if d^2 >= m then return (d - m/d)^2 fi
  od
end proc:
map(f, TA); # Robert Israel, Apr 09 2025

a(n) = A108945(n) - A001359(n) - A006512(n).

a(n) = (A033677(A040040(n)) - A040040(n)/A033677(A040040(n)))^2. - Robert Israel, Apr 09 2025

Edited and extended by Ray Chandler, Jul 25 2005

A108945 Squares equal to the sum of the n-th twin prime pair and minimal square k^2.

Original entry on oeis.org

9, 16, 25, 36, 64, 100, 121, 144, 400, 225, 676, 400, 361, 400, 400, 625, 484, 576, 2500, 625, 1225, 841, 900, 1024, 1444, 1156, 1225, 11236, 12100, 1369, 1764, 19600, 1681, 2116, 1764, 2209, 3025, 2116, 4624, 2209, 2304, 3136, 6400, 3364, 2704, 2704, 3025

Offset: 1

Giovanni Teofilatto, Jul 21 2005

nonn

			a(1) = 9 because 3+5+1=9;
a(2) = 16 because 5+7+4=16;
a(3) = 25 because 11+13+1=25;
a(4) = 36 because 17+19+0=36.

Cf. A001359, A006512, A108943, A108944.

a(n) = A001359(n) + A006512(n) + A108944(n).

Edited and extended by Ray Chandler, Jul 25 2005

cp's OEIS Frontend

A108944 Minimal square k^2 such that sum of the n-th twin prime pair plus k^2 is a square.

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