A181429 a(n)= the smallest number such that a(n)^2+1=p*A002144(n), p prime.

3, 5, 30, 12, 80, 9, 30, 11, 46, 34, 22, 414, 76, 15, 100, 44, 28, 80, 19, 274, 380, 794, 144, 64, 530, 456, 60, 334, 724, 25, 114, 526, 136, 42, 104, 274, 334, 1584, 266, 29, 254, 516, 566, 48, 810, 286, 52, 2110, 86, 1130, 516, 726, 35, 194, 154, 504, 106, 58, 4036, 566, 96, 380

Offset: 1

Author

Michel Lagneau, Jan 29 2011

Keywords

• nonn

Examples

			a(1) = 3 because 3^2+1 = 2*A002144(1) = 2*5 ;
a(2) = 5 because 5^2+1 = 2*A002144(2) = 2*13 ;
a(3) = 30 because 30^2+1 = 53*A002144(3)  = 53*17;
a(4) = 12 because 12^2+1 = 5*A002144(4) = 5*29.
		

Crossrefs

Cf. A002144.

Programs

Maple

with(numtheory):nn:=10000:T:=array(1..10000):k:=2:T[1]:=2: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
  2 to 100 do: id:=0:for p from 1 to k while(id=0) do:x:=T[n]*T[p]-1:y:=sqrt(x):if
  y=floor(y)then id:=1:printf(`%d, `,y):else fi:od:od: