A034700 - OEIS

%I #21 Aug 09 2018 10:44:01

%S 5,29,109,281,349,1601,1889,5581,12421,14389,16829,89501,294761,

%T 471781,1134389,2465081,2708941,4695809,9594709,33660421,38692009,

%U 75670769,138202481,150274469,517777769,3675456101,4720745641,27541365749,29340233569,69737217721,112295532029

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

%C 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.

%t 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 *)

%o (Haskell)

%o a034700 n = a034700_list !! (n-1)

%o a034700_list = f [1,5..] [1] where

%o    f (x:xs) ys | a010051' x == 1 &&

%o                  (and $ map (isSquMod x) ys) = x : f xs (x:ys)

%o                | otherwise                   = f xs ys

%o    isSquMod u v = v `mod` u `elem` (map ((`mod` u) . (^ 2)) [0..u-1])

%o -- _Reinhard Zumkeller_, Mar 28 2012

%Y Cf. A034698.

%Y Cf. A010051, A002144, A034791.

%K nonn,nice

%O 1,1

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

%E More terms from _David W. Wilson_

%E a(26)-a(31) from _Giovanni Resta_, Aug 09 2018