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

1,1

Comments

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

Links

Table of n, a(n) for n=1..44.

Example

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.

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:

Crossrefs

Cf. A002522, A002496, A238138, A238139.

Sequence in context: A230812 A087938 A103729 * A027862 A308442 A322155

Adjacent sequences: A234736 A234737 A234738 * A234740 A234741 A234742

Keyword

nonn

Author

Michel Lagneau, Dec 30 2013

Status

approved