A077035 a(1)=7; a(n),a(n+1) are smallest > a(n-1) such that a(n-1)^2+a(n)^2=a(n+1)^2.

7, 24, 25, 60, 65, 72, 97, 4704, 4705, 11292, 12233, 79044, 79985, 124212, 147737, 430416, 455065, 504072, 679097, 24502296, 24511705, 34278300, 42140545, 68012700, 80009705, 192023292, 208025233, 356427144, 412692145, 990461148, 1072999577, 2403086064, 2631758105

Offset

1,1

Comments

Note that each time two more terms are added simultaneously.

Links

Table of n, a(n) for n=1..33.

Example

a(1)=7 therefore a(2)=24 and a(3)=25: 7^2+24^2=25^2; a(3)=25 therefore a(4)=60 and a(5)=65: 25^2+60^2=65^2.

Prog

(Python)
from math import isqrt
from sympy.ntheory.primetest import is_square
def aupton(terms):
    alst = [7]
    for n in range(2, terms+1, 2):
        sq1, an = alst[-1]**2, alst[-1] + 1
        while not is_square(sq1 + an**2): an += 1
        alst.extend([an, isqrt(sq1 + an**2)])
    return alst[:terms]
print(aupton(19)) # Michael S. Branicky, Jul 24 2021

Crossrefs

Cf. A077034, A076604.

Sequence in context: A286406 A070410 A377011 * A076602 A287132 A287193

Adjacent sequences: A077032 A077033 A077034 * A077036 A077037 A077038

Keyword

nonn

Author

Zak Seidov, Oct 21 2002

Extensions

a(16) and beyond from Michael S. Branicky, Jul 24 2021

Status

approved