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A211175 Triangle read by rows: row n gives, in increasing order, the prime divisors of all the composites of the form k^2 + 1 between the two primes A002496(n) and A002496(n+1).

%I A211175 #31 Jul 03 2022 04:52:50
%S A211175 2,5,2,13,2,5,13,41,2,5,17,29,61,2,113,2,5,13,29,181,2,5,13,17,53,97,
%T A211175 2,313,2,5,13,17,37,41,53,73,89,109,157,421,613,2,5,17,137,761,2,5,13,
%U A211175 17,29,37,41,61,73,149,281,353,461,541,1013,1201,1301,2,17
%N A211175 Triangle read by rows: row n gives, in increasing order, the prime divisors of all the composites of the form k^2 + 1 between the two primes A002496(n) and A002496(n+1).
%C A211175 A variety of conjecturally infinite subsequences and starting with {2, 5, ...} can be shown in the graph of the sequence. If the number of primes of the form n^2 + 1 is finite, then the last subsubsequence of the graph abruptly becomes A002144(n) union {2} (odd Pythagorean primes with the number 2). In this case, the discontinued forms of the graph disappear. But this case is highly improbable.
%H A211175 Michel Lagneau, <a href="/A211175/b211175.txt">Rows n = 2..557 of irregular triangle, flattened</a>
%e A211175 The irregular triangle of divisors is:
%e A211175 [2, 5]
%e A211175 [2, 13]
%e A211175 [2, 5, 13, 41]
%e A211175 [2, 5, 17, 29, 61]
%e A211175 [2, 113]
%e A211175 [2, 5, 13, 17, 53, 97]
%e A211175 ...
%e A211175 Row 1 is empty because there are no numbers of the form k^2 + 1 between A002496(1) = 2 and A002496(2) = 5.
%e A211175 row 2 = [2, 5] lists divisors of 3^2 + 1 between the primes A002496(2) and A002496(3);
%e A211175 row 3 = [2, 13] lists divisors of 5^2 + 1 between the primes A002496(3) and A002496(4);
%e A211175 row 4 = [2, 5, 13, 41] lists divisors of 7^2 + 1, 8^2 + 1, 9^2 + 1 between the primes A002496(4) and A002496(5).
%p A211175 with(numtheory) :lst:={}: for n from 2 to 150 do:p:=n^2+1:x:=factorset(p):lst:=lst union x:if type(p,prime)=true then print(lst minus {p}):lst:={}:else fi:od:
%Y A211175 Cf. A002144, A002496, A002522, A134406, A181413, A206400.
%K A211175 nonn,tabf
%O A211175 2,1
%A A211175 _Michel Lagneau_, Feb 01 2013