A059321 Smallest number m such that m^2+1 is divisible by A002144(n)^2 (= squares of primes congruent to 1 mod 4).

7, 70, 38, 41, 117, 378, 500, 682, 776, 3861, 4052, 515, 5744, 1710, 6613, 1744, 11018, 13241, 3458, 5099, 1393, 16610, 26884, 15006, 2072, 13637, 31361, 4443, 26508, 7850, 37520, 31152, 39922, 37107, 6072, 4005, 32491, 4030, 43211, 12238

Offset

1,1

Comments

a(2) = 70 since A002144(2)=13, 70^2+1 = 4091 = 13^2 * 29 and for no k<70 does 13^2 divide k^2+1. Related to period-1 continued fractions.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..2000 from Klaus Brockhaus)

Prog

(Python)
from itertools import islice
from sympy import nextprime, sqrt_mod_iter
def A059321_gen(): # generator of terms
    p = 1
    while (p:=nextprime(p)):
        if p&3==1:
            yield min(sqrt_mod_iter(-1, p**2))
A059321_list = list(islice(A059321_gen(), 20)) # Chai Wah Wu, May 04 2024

Crossrefs

Cf. A002144, A059591, A059592.

Sequence in context: A226270 A121351 A302353 * A217400 A077683 A082797

Adjacent sequences: A059318 A059319 A059320 * A059322 A059323 A059324

Keyword

easy,nonn

Author

Marc LeBrun, Jan 26 2001

Status

approved