A385050 a(n) is the least positive number k such that n is the greatest m such that k is a quadratic residue mod prime(i) for i=1..m and {k mod prime(i): i=1..m} are all distinct.
1, 3, 4, 184, 9, 1479, 20799, 31509, 162094, 83554, 828844, 895449, 4631104, 86925309, 97476129, 14684224, 33547264, 5381151099, 516743824, 1958770564, 112746608529, 3046156864, 373079083204, 1394424964, 297469886464, 1596601563489, 976001733184, 33344131402059
Offset: 1
Keywords
Examples
a(1) = 1: |{1}| = 1: 1 mod 2 = 1^2 mod 2, terminates at 1 mod 3 (not distinct: repeats 1 mod 2).
a(2) = 3: |{1, 0}| = 2: 3 mod 2 = 1^2 mod 2, 3 mod 3 = 0^2 mod 3, terminates at 3 mod 5 (nonsquare).
a(3) = 4: |{0, 1, 4}| = 3.
a(4) = 184: |{0, 1, 4, 2}| = 4 (2 = 3^2 mod 7).
a(5) = 9: |{1, 0, 4, 2, 9}| = 5.
a(6) = 1479: |{1, 0, 4, 2, 5, 10}| = 6.
Crossrefs
Programs
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PARI
a(n)={my(v=List); for(k=1, oo, my(m=Map); for(i=1, oo, my(p=prime(i), kp=k%p); if(i>#v, listput(v, Map); for(j=0, (p-p%2)/2, mapput(v[i], j^2%p, 1))); if(mapisdefined(v[i], kp) && !mapisdefined(m, kp), mapput(m, kp, 1); next); if(i-1==n, return(k)); break))}
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