OFFSET
1,1
COMMENTS
For L(p(i)/p(j)) = 1 see A276525.
L(x/y) = L(y/x) for primes x, y, and either x=4r+1 for some r, or y=4r+1 for some r.
We observe pairs of the form (a(n), a(n)+1) with a(n): 35, 44, 50, 51, 74, 75, 85, 86, 87, 90, 115, 118, 119, 122, 134, 143, ...
We observe triples of the form (a(n), a(n)+1, a(n)+2) with a(n): 50, 74, 85, 86, 118, 174, 214, 260, 286, 318, 324, 403, 484, 634, 635, ...
We observe quadruplets of the form (a(n), a(n)+1, a(n)+2, a(n)+3) with a(n): 85, 634, 635, 696, 842, 1340, 1382, 2424, 2599, 2929, 3145, 3576, ...
We observe quintuplets of the form (a(n), a(n)+1, a(n)+2, a(n)+3, a(n)+4) with a(n): 634, 10951, 12184, 20281, 21967, 29493, ...
We observe sextuplets of the form (a(n), a(n)+1, a(n)+2, a(n)+3, a(n)+4), a(n)+5) with a(n): 60747, 742582, ...
LINKS
Michel Lagneau, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Legendre Symbol
EXAMPLE
10 is in the sequence because the prime factors are 2 and 5 => L(2,5) = L(5,2) = -1.
275070 is in the sequence because the prime factors are 2, 3, 5, 53 and 173 => L(2,3) = L(2,5) = L(2,53) = L(2,173) = L(3,5) = L(3,53) = L(3,173) = L(5,53) = L(5,173) = L(53,173) = L(173,53) = L(173,5) = L(173,3) = L(173,2) = L(53,5) = L(53,3) = L(53,2) = L(5,3) = L(5,2) = L(3,2) = -1.
MATHEMATICA
fQ[n_] := If[!PrimeQ@ n, Block[{pf = Transpose[ FactorInteger[n]][[1]]}, lng = Length@ pf; Union[ Flatten[ Table[ JacobiSymbol[pf[[i]], pf[[j]]], {i, lng}, {j, lng}]]] == {-1, 0}], False]; Select[ Range@ 330, fQ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Dec 15 2016
STATUS
approved