A174492 a(n) = the smallest k such that k^2+1 = p*A002144(n)^2, p prime of A002144 .

18, 70, 540, 800, 1486, 2984, 500, 6760, 776, 4060, 5604, 4030, 5744, 1710, 1744, 46146, 186174, 162886, 62064, 32150, 37416, 16610, 26884, 15006, 130026, 58724

Offset: 1

Author

Michel Lagneau, Jan 25 2011

Keywords

• nonn

Comments

A002144 are the primes of the form 4q + 1.

Examples

			a(1) = 18 because 18^2 + 1 = 13*A002144(1) ^2 = 13*5^2 ;
a(2) = 70 because 70^2 + 1 = 29*A002144(2) ^2 = 29*13^2 ;
a(3) = 540 because 540^2 + 1 = 1009*A002144(3) ^2 = 1009*17^2 .
		

Crossrefs

Cf. A002144 A059321.

Programs

Maple

with(numtheory):nn:=400:T:=array(1..nn):k:=1:for x from 1 to nn do: p:=4*x+1:if
  type(p,prime)=true then T[k]:=p:k:=k+1:else fi:od:for n from 1 to k do: ind:=0:for
  m from 1 to 500000 while(ind=0) do:y:=m^2+1:x:= factorset(y) : n1:=nops(x):n2
  :=bigomega(y):if n1=2 and n2 = 3 and x[1]=T[n] and ind=0 then ind:=1:printf(`%d,
  `,m):else fi:od:od: