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A234739 Largest prime divisor of all composite numbers of the form k^2+1 between two consecutive primes of the same form. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 17 16:38 EDT 2019. Contains 325107 sequences. (Running on oeis4.)