A234739 Largest prime divisor of all composite numbers of the form k^2+1 between two consecutive primes of the same form.

5, 13, 41, 61, 113, 181, 97, 313, 613, 761, 1301, 89, 2113, 2521, 3121, 3613, 1693, 5101, 1277, 557, 7321, 601, 1613, 8581, 10513, 2161, 4621, 12641, 14281, 15313, 6337, 16381, 20201, 21013, 21841, 24421, 5153, 26681, 11329, 30013, 977, 13313, 34061, 7129

Offset: 1

Author

Michel Lagneau, Dec 30 2013

Keywords

• nonn

Comments

Or, largest of all prime factors of composite numbers in A002522 between two consecutive primes A002496(n) and A002496(n+1).

Examples

			181 is in the sequence because the composites between the two primes A002496(7)= 16^2+1 = 257 and A002496(8)= 20^2+1=401 are: 17^2+1= 2*5*29; 18^2+1 = 5*5*13; 19^2+1=2*181 and the largest prime divisor is 181, so a(5)=181.
		

Crossrefs

Cf. A002522, A002496, A238138, A238139.

Programs

Maple

with(numtheory):T:=array(1..111):k:=0:for n from 2 by 2 to 1000 do: p:=n^2+1:if type(p,prime)=true then k:=k+1:T[k]:=p:else fi:od:for i from 1 to k do:d0:=0:a:=sqrt(T[i]-1):b:=sqrt(T[i+1]-1):for j from a+1 to b-1 do:y:=factorset(j^2+1):n1:=nops(y):d:=y[n1]:if d>d0 then d0:=d:else fi:od: printf(`%d, `,d0):od: