A135596 Number of positive solutions of the Diophantine x*p+y*q=p^3+q^3, where p=n-th prime, q=(n+1)-th prime.

6, 10, 13, 22, 25, 32, 37, 43, 55, 61, 70, 79, 85, 91, 101, 113, 121, 129, 139, 145, 153, 163, 173, 187, 199, 205, 211, 217, 223, 243, 259, 269, 277, 289, 301, 309, 321, 331, 341, 353, 361, 373, 385, 391, 397, 411, 435, 451, 457, 463, 473, 481, 493, 509, 521

Offset

1,1

Links

Table of n, a(n) for n=1..55.

Example

a(1)=6 because Diophantine 2x+3y=2^3+3^3 has 6 positive solutions {x,y}:
{1, 11}, {4, 9}, {7, 7}, {10, 5}, {13, 3}, {16, 1};
a(2)=10 because Diophantine 3x+5y=3^3+5^3 has 10 positive solutions {x, y}:
{4, 28}, {9, 25}, {14, 22}, {19, 19}, {24, 16}, {29, 13}, {34, 10}, {39, 7}, {44, 4}, {49, 1};
a(3)=13 because Diophantine 5x+7y=5^3+7^3 has 13 positive solutions {x, y}:
{4, 64}, {11, 59}, {18, 54}, {25, 49}, {32, 44}, {39, 39}, {46, 34}, {53, 29}, {60, 24}, {67, 19}, {74, 14}, {81, 9}, {88, 4}.

Mathematica

Table[With[{p=Prime[n], q=Prime[n+1]}, Floor[q^2/p]+Floor[p^2/q]+1], {n, 1, 100}]

Crossrefs

Sequence in context: A315155 A315156 A315157 * A233456 A189762 A163814

Adjacent sequences: A135593 A135594 A135595 * A135597 A135598 A135599

Keyword

nonn

Author

Zak Seidov, Feb 26 2008

Status

approved