A034795 - OEIS

%I #18 Dec 30 2024 13:14:13

%S 2,3,7,11,23,29,53,59,71,73,79,83,109,113,127,131,151,167,173,179,191,

%T 193,197,223,227,239,241,251,263,269,283,293,307,311,313,317,353,383,

%U 389,409,419,431,433,439,443,457,461,467,479,487,491,503,509,523,547

%N a(n) is the least prime > a(n-1) that is a quadratic residue mod a(n-1).

%H Robert Israel, <a href="/A034795/b034795.txt">Table of n, a(n) for n = 1..10000</a>

%p f:= proc(p) local q;

%p    q:= p;

%p    do

%p      q:= nextprime(q);

%p      if NumberTheory:-QuadraticResidue(q,p)=1 then return q fi

%p    od

%p end proc:

%p A[1]:= 2: for i from 2 to 100 do A[i]:= f(A[i-1]) od:

%p seq(A[i],i=1..100); # _Robert Israel_, Jan 06 2023

%t a[1] = 2; a[2] = 3; a[n_] := a[n] = For[p = NextPrime[a[n-1]], True, p = NextPrime[p], If[JacobiSymbol[p, a[n-1]] == 1, Return[p]]];

%t a /@ Range[55] (* _Jean-François Alcover_, Dec 28 2019 *)

%t lpqr[n_]:=Module[{p=NextPrime[n]},While[JacobiSymbol[p,n]==-1,p=NextPrime[p]];p]; Join[{2},NestList[lpqr,3,60]] (* _Harvey P. Dale_, Dec 30 2024 *)

%Y Cf. A034795.

%K nonn,nice

%O 1,1

%A _David W. Wilson_

%E Name corrected by _Robert Israel_, Jan 06 2023