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 A034698 a(n) is the smallest prime such that a(1), ..., a(n-1) are squares mod a(n). 3
 2, 7, 31, 113, 233, 647, 1487, 4919, 6329, 7951, 26833, 47737, 53623, 128959, 135697, 142327, 1312777, 3178289, 6061607, 26564393, 32426081, 102958417, 209074609, 323901311, 587709359, 1006009759, 1029482303, 9876033449, 11061524183, 15821898167, 27926616007 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Giovanni Resta, Table of n, a(n) for n = 1..39 MATHEMATICA residueQ[n_, p_] := JacobiSymbol[n, p] == 1; a[1] = 2;  a[n_] := a[n] = For[r = Range[n - 1]; p = NextPrime[a[n - 1]], True, p = NextPrime[p], If[AllTrue[r, residueQ[a[#], p] &], Return[p]]]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 24}] (* Jean-François Alcover, Feb 16 2018 *) PROG (Haskell) a034698 n = a034698_list !! (n-1) a034698_list = f [2..] [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 (PARI) first(n) = my(res=vector(n)); res[1]=2; for(x=2, n, forprime(p=res[x-1]+1, , for(y=1, x-1, if(!issquare(Mod(res[y], p)), next(2))); res[x]=p; break())); res \\ Iain Fox, Aug 08 2018 (PARI) nextterm(v) = forprime(p=v[#v]+1, , for(y=1, #v, if(!issquare(Mod(v[y], p)), next(2))); return(p)) \\ (Inserting a vector of the first n-1 terms will return the n-th term) Iain Fox, Aug 08 2018 CROSSREFS Cf. A034700. Cf. A010051, A034791. Sequence in context: A213721 A102162 A059846 * A115605 A289719 A114198 Adjacent sequences:  A034695 A034696 A034697 * A034699 A034700 A034701 KEYWORD nonn,nice AUTHOR E. M. Rains (rains(AT)caltech.edu) EXTENSIONS More terms from David W. Wilson a(25)-a(28) from Iain Fox, Aug 08 2018 a(29)-a(30) from Iain Fox, Aug 09 2018 a(31) from Iain Fox, Aug 10 2018 STATUS approved

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Last modified January 20 12:32 EST 2019. Contains 319330 sequences. (Running on oeis4.)