(MAGMAMagma) SmallestP:=function(n) for p in PrimesUpTo(1000) do if IsPrime(p + n*(n+1) div 2) then return p; end if; end for; return 0; end function; [SmallestP(n): n in [0..100]]; // Klaus Brockhaus, Apr 10 2010

(MAGMAMagma) SmallestQ:=function(n) for m in PrimesUpTo(1000) do E:=Eigenvalues(Matrix([&cat[ [j ne k select j else m+j]: k in [1..n]]: j in [1..n] ])); if forall(t){x: x in E | IsPrime(x[1])} then return m; end if; end for; return 0; end function; [2] cat [SmallestQ(n): n in [1..100]]; // Klaus Brockhaus, Apr 10 2010

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J.-M. Monier, Algebre et geometrie, exercices corriges. Dunod, 1997, p. 78.

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Smallest prime p such that p + n*(n+1)/2 is prime, or 0 if no such prime exists.

(MAGMA) SmallestP:=function(n) for p in PrimesUpTo(1000) do if IsPrime(p + n*(n+1) div 2) then return p; end if; end for; return 0; end function; [ SmallestP(n): n in [0..100] ]; // Klaus Brockhaus, Apr 10 2010

(MAGMA) SmallestQ:=function(n) for m in PrimesUpTo(1000) do E:=Eigenvalues( Matrix([ &cat[ [j ne k select j else m+j]: k in [1..n] ]: j in [1..n] ]) ); if forall(t){ x: x in E | IsPrime(x[1]) } then return m; end if; end for; return 0; end function; [2] cat [ SmallestQ(n): n in [1..100] ]; // Klaus Brockhaus, Apr 10 2010

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(MAGMA) SmallestP:=function(n) for p in PrimesUpTo(1000) do if IsPrime(p + n*(n+1) div 2) then return p; end if; end for; return 0; end function; [ SmallestP(n): n in [0..100] ]; [From // _Klaus Brockhaus, _, Apr 10 2010]

(MAGMA) SmallestQ:=function(n) for m in PrimesUpTo(1000) do E:=Eigenvalues( Matrix([ &cat[ [j ne k select j else m+j]: k in [1..n] ]: j in [1..n] ]) ); if forall(t){ x: x in E | IsPrime(x[1]) } then return m; end if; end for; return 0; end function; [2] cat [ SmallestQ(n): n in [1..100] ]; [From // _Klaus Brockhaus, _, Apr 10 2010]

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a[n_] := (p = 2; q = n*(n+1)/2; While[p > 0, If[ PrimeQ[p+q], Break[], p = If[ OddQ[q], 0, NextPrime[p]]]]; p); Table[a[n], {n, 0, 100}] (* From _Jean-François Alcover, _, Nov 03 2011 *)

_Michel Lagneau (mn.lagneau2(AT)orange.fr), _, Apr 02 2010

Edited and corrected by _Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), _, Apr 10 2010