A094048 Let p(n) be the n-th prime congruent to 1 mod 4. Then a(n) = the least m for which m^2+1=p(n)*k^2 has a solution.

2, 18, 4, 70, 6, 32, 182, 29718, 1068, 500, 5604, 10, 8890182, 776, 1744, 113582, 4832118, 1118, 1111225770, 1764132, 14, 1710, 23156, 71011068, 16, 82, 8920484118, 1063532, 2482, 126862368, 352618, 1015827336, 9210, 71264, 5118, 1282, 20478302982, 20, 111921796968, 44042445696821418

Offset

1,1

Comments

Subsequence of A191860. - Reinhard Zumkeller, Jun 18 2011

Links

Table of n, a(n) for n=1..40.

Mathematica

f[n_] := Block[{y = 1}, While[ !IntegerQ[ Sqrt[n*y^2 - 1]], y++ ]; Sqrt[n*y^2 - 1]]; lst = {}; Do[p = Prime@ n; If[ Mod[p, 4] == 1, AppendTo[lst, f@p]; Print[{n, Prime@n, f@p}]], {n, 66}]; lst

Prog

(Haskell)
a094048 n = head [m | m <- map (a037213 . subtract 1 . (* a002144 n))
                               (tail a000290_list), m > 0]
-- Reinhard Zumkeller, Jun 13 2015
(Python)
from itertools import count, islice
from sympy.solvers.diophantine.diophantine import diop_DN
from sympy import isprime
def A094048_gen(): # generator of terms
    for n in count(1, 4):
        if isprime(n):
            yield min(a[0] for a in diop_DN(n, -1))
A094048_list = list(islice(A094048_gen(), 52)) # Chai Wah Wu, Dec 22 2025

Crossrefs

Cf. A002144, A094049 (associated k), A130226, A137351, A179073.

Cf. A000196, A037213, A000290.

Sequence in context: A113918 A383240 A253603 * A387642 A179073 A087665

Adjacent sequences: A094045 A094046 A094047 * A094049 A094050 A094051

Keyword

nonn

Author

Matthijs Coster, Apr 29 2004

Extensions

Edited by Don Reble, Apr 30 2004

More terms from Michel Marcus, Dec 23 2025

Status

approved