The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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). 3
 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, 2, 313, 2, 5, 13, 17, 37, 41, 53, 73, 89, 109, 157, 421, 613, 2, 5, 17, 137, 761, 2, 5, 13, 17, 29, 37, 41, 61, 73, 149, 281, 353, 461, 541, 1013, 1201, 1301, 2, 17 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS 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 becomes abruptly 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. LINKS Michel Lagneau, Rows n = 2..557 of irregular triangle, flattened EXAMPLE The irregular triangle of divisors is: [2, 5] [2, 13] [2, 5, 13, 41] [2, 5, 17, 29, 61] [2, 113] [2, 5, 13, 17, 53, 97] ... Row 1 is empty because there are no numbers of the form k^2 + 1 between A002496(1) = 2 and A002496(2) = 5. row 2 = [2, 5] lists divisors of 3^2 + 1 between the primes A002496(2) and A002496(3); row 3 = [2, 13] lists divisors of 5^2 + 1 between the primes A002496(3) and A002496(4); 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). MAPLE 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: CROSSREFS Cf. A002144, A002496, A002522, A134406, A181413, A206400. Sequence in context: A207635 A205715 A181338 * A102469 A098886 A286785 Adjacent sequences:  A211172 A211173 A211174 * A211176 A211177 A211178 KEYWORD nonn,tabf AUTHOR Michel Lagneau, Feb 01 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 30 23:12 EDT 2021. Contains 346365 sequences. (Running on oeis4.)