A034700 a(n) = smallest prime == 1 (mod 4) such that a(n) is a square mod a(i), all i<n.

5, 29, 109, 281, 349, 1601, 1889, 5581, 12421, 14389, 16829, 89501, 294761, 471781, 1134389, 2465081, 2708941, 4695809, 9594709, 33660421, 38692009, 75670769, 138202481, 150274469, 517777769, 3675456101, 4720745641, 27541365749, 29340233569, 69737217721, 112295532029

Offset

1,1

Comments

a(n) is also smallest prime == 1 (mod 4) such that a(i) is a square mod a(n), all i<n. Thus each a(i) is a square mod each a(j), i<>j.

Links

Table of n, a(n) for n=1..31.

Mathematica

next[p_] := If[ Mod[np = NextPrime[p], 4] != 1, next[np], np]; s = {next[2]}; Print[ s[[1]] ]; squareModQ[p_, q_] := (Reduce[ Mod[p - x^2, q] == 0, x, Integers] =!= False); ok[p_] := (r = True; Do[ If[ squareModQ[p, s[[k]] ] === False, r = False; Break[] ], {k, 1, Length[s]} ]; r); grow := (p = next[ Last[s] ]; While[ ok[p] === False, p = next[p] ]; Print[p]; AppendTo[s, p]); Do[ grow, {24} ]; A034700 = s (* Jean-François Alcover, Apr 04 2012 *)

Prog

(Haskell)
a034700 n = a034700_list !! (n-1)
a034700_list = f [1, 5..] [1] where
   f (x:xs) ys | a010051' x == 1 &&
                 (and $ map (isSquMod x) ys) = x : f xs (x:ys)
               | otherwise                   = f xs ys
   isSquMod u v = v `mod` u `elem` (map ((`mod` u) . (^ 2)) [0..u-1])
-- Reinhard Zumkeller, Mar 28 2012

Crossrefs

Cf. A034698.

Cf. A010051, A002144, A034791.

Sequence in context: A097345 A097344 A153076 * A057721 A085151 A119494

Adjacent sequences: A034697 A034698 A034699 * A034701 A034702 A034703

Keyword

nonn,nice

Author

E. M. Rains (rains(AT)caltech.edu)

Extensions

More terms from David W. Wilson

a(26)-a(31) from Giovanni Resta, Aug 09 2018

Status

approved