A034791 a(n) is square mod a(i), i < n.

1, 2, 7, 14, 31, 62, 113, 226, 233, 466, 647, 1294, 1487, 2974, 4919, 6329, 7951, 12658, 15902, 26329, 26833, 47737, 52658, 53623, 53666, 95474, 107246, 128959, 135697, 142327, 271394, 284654, 715177, 1312777, 1430354, 1474657, 2625554

Offset

1,2

Comments

Apparently A034698 is a subsequence and all elements are products of elements of A034698.

a(n) is the smallest integer larger than a(n-1) such that all a(i), 1<=i<n, are quadratic residues mod a(n). - R. J. Mathar, Jul 27 2015

Links

Table of n, a(n) for n=1..37.

Maple

A034791 := proc(n)
    option remember;
    local a, wrks ;
    if n = 1 then
        1;
    else
        for a from procname(n-1)+1 do
            wrks := true;
            for i from 1 to n-1 do
                if numtheory[quadres](procname(i), a) <> 1 then
                    wrks := false;
                end if;
            end do;
            if wrks then
                return a;
            end if;
        end do:
    end  if;
end proc: # R. J. Mathar, Jul 27 2015

Mathematica

residueQ[n_, k_] := Length[Select[Range[Floor[k/2]], PowerMod[#, 2, k] == n &, 1]] == 1; a[1] = 1; a[n_] := a[n] = For[r = Range[n - 1]; an = a[n - 1] + 1, True, an++, If[AllTrue[r, residueQ[a[#], an] &], Return[an]]]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 37}] (* Jean-François Alcover, Feb 16 2018 *)

Prog

(Haskell)
a034791 n = a034791_list !! (n-1)
a034791_list = 1 : f [2..] [1] where
   f (x:xs) ys | and $ map (flip isSquMod x) ys = x : f xs (x:ys)
               | otherwise                      = f xs ys
   isSquMod u v = u `mod` v `elem` (map ((`mod` v) . (^ 2)) [0..v-1])
-- Reinhard Zumkeller, fixed Jul 29 2015, Mar 28 2012

Crossrefs

Cf. A034698.

Cf. A034793, A034903.

Sequence in context: A221235 A224916 A258321 * A140253 A018453 A286829

Adjacent sequences: A034788 A034789 A034790 * A034792 A034793 A034794

Keyword

nonn

Author

David W. Wilson

Status

approved