A034698 a(n) is the smallest prime such that a(1), ..., a(n-1) are squares mod a(n).

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

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: A102162 A059846 A343532 * 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