A349665 Record terms of A349664.

0, 1, 2, 3, 7, 17, 27, 37, 87, 137, 157, 187, 247, 437, 687, 787, 937, 1237, 2187, 3437, 3937, 4687, 6187, 8437, 10937, 17187, 19687, 23437, 30937, 42187, 54687, 55687, 85937, 98437, 117187, 154687, 210937, 223437, 273437, 278437, 304687, 429687, 492187, 585937

Offset

1,3

Comments

Terms are the record numbers of solutions for the equation: y^4 = z^2 - x^2.

Links

Table of n, a(n) for n=1..44.

Karl-Heinz Hofmann, Full table up to y <= 10^12

Example

Number of | y | Factorization
solutions |   |      of y
----------+---+--------------
        0 | 1 |  -
        1 | 2 | [2]
        2 | 3 | [3]
        3 | 4 | [2, 2]
        7 | 6 | [2, 3]
        :   :      :
For more terms with y and factorization of y see link.

Prog

(PARI) lista(nn) = my(f, r); print1("0, 1, 2"); forstep(n=4, nn, 2, f=factor(n)[, 2]; if(r<f=prod(k=2, #f, 4*f[k]+1)*(4*f[1]-1), print1(", ", (r=f)\2))); \\ Jinyuan Wang, Dec 19 2021

Crossrefs

Cf. A000290, A000583, A002144, A002145, A271576, A346115, A349663.

Sequence in context: A338175 A268539 A083822 * A030086 A078721 A077007

Adjacent sequences: A349662 A349663 A349664 * A349666 A349667 A349668

Keyword

nonn

Author

Karl-Heinz Hofmann, Dec 18 2021

Extensions

More terms from Jinyuan Wang, Dec 19 2021

Status

approved