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%I #23 Sep 04 2023 14:32:03
%S 2,7,113,233,337,2129,3833,8737,19553,46337,72689,103681,361649,
%T 449689,477017,668273,3095353,7212577,13188281,26340857,46012633,
%U 246116833,330177017,354681097,1014496289,1315295809,2269762961,4651240801,14947292497
%N a(i) is a square mod a(j), i <> j; a(n) prime; a(1) = 2.
%t a[1] = 2; squareModQ[p_, q_] := (For[k=0, k <= q, k++, If[Mod[p-k^2, q] == 0, Return[True]]]; Return[False]); a[n_] := a[n] = For[r=NextPrime[a[n-1]], True, r=NextPrime[r], If[And @@ (squareModQ[r, #] && squareModQ[#, r] & /@ Array[a, n-1]), Return[r]]]; Table[Print[a[n]]; a[n], {n, 1, 10}] (* _Jean-François Alcover_, Dec 10 2014 *)
%o (PARI) isok(newp, v, n) = {for (k=1, n, if (!issquare(Mod(newp, v[k])) || !issquare(Mod(v[k], newp)), return (0));); return (1);}
%o lista(nn) = {my(v=vector(nn), lastp=2); v[1] = lastp; for (n=2, nn, my(newp = nextprime(lastp+1)); while (! isok(newp, v, n-1), newp = nextprime(newp+1)); v[n] = newp; lastp = newp;); v;} \\ _Michel Marcus_, Sep 25 2020
%Y Cf. A034900, A034901.
%K nonn,nice,more
%O 1,1
%A _David W. Wilson_
%E a(24)-a(29) from _Sean A. Irvine_, Sep 20 2020
%E Name edited by _Michel Marcus_, Sep 24 2020