A103248
Numbers x, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers.
Original entry on oeis.org
16, 24, 36, 44, 56, 60, 64, 68, 76, 84, 88, 92, 96, 100, 104, 116, 120, 124, 128, 132, 136, 140, 144, 152, 156, 160, 164, 168, 172, 176, 184, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228, 236, 240, 244, 252, 256, 264, 272, 276, 280, 284, 288, 296, 300, 304
Offset: 1
x=16, y=63, 16^2 + 63^2 = 65^2. 16 is the 1st entry in the list.
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pythtri(n) = { local(a,b,c=0,k,x,y,z,vx,vy,wx,wyj); wx=wy= vector(n*n); for(a=1,n, for(b=1,n, x=2*a*b; y=b^2-a^2; z=b^2+a^2; if(y > 0 &!isprime(x) &!isprime(y) &!isprime(z), if(gcd(x,y)==1&gcd(x,z)==1&gcd(y,z)==1, c++; wy[c]=y; wx[c]=x; print(x","y","z); \ write("pythtri.txt",x","y","z); ) ) ) ); vy=vx=vector(c); wy=vecsort(wy); wx=vecsort(wx); for(j=1,n*n, if(wx[j]>0, k++; vx[k]=wx[j]; ); ); for(j=1,200, if(vx[j+1]<>vx[j],print1(vx[j]",")) ) }
A103251
Numbers x, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers and z is a perfect square.
Original entry on oeis.org
24, 96, 120, 216, 240, 336, 384, 480, 600, 720, 840, 840, 864, 960, 1080, 1176, 1320, 1344, 1536, 1920, 1944, 2016, 2160, 2184, 2400, 2520, 2880, 2904, 3000, 3024, 3360, 3360, 3360, 3456, 3696, 3840, 3960, 4056, 4320, 4704, 4896, 5280, 5280, 5376, 5400
Offset: 1
x=24, y=7, 24^2 + 7^2 = 25^2. 24 is the 1st entry in the list.
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pythtrisq(n) = { local(a,b,c=0,k,x,y,z,vy,wx,vx,vz,j); w = vector(n*n+1); for(a=1,n, for(b=1,n, x=2*a*b; y=b^2-a^2; z=b^2+a^2; if(y > 0 & issquare(z), c++; w[c]=x; print(x","y","z) ) ) ); vx=vector(c); w=vecsort(w); for(j=1,n*n, if(w[j]>0, k++; vx[k]=w[j]; ) ); for(j=1,200, print1(vx[j]",") ) }
A103249
Numbers y, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers and x is a perfect square.
Original entry on oeis.org
3, 12, 17, 27, 48, 63, 68, 75, 77, 99, 108, 147, 153, 192, 243, 252, 272, 300, 301, 308, 323, 363, 396, 399, 425, 432, 507, 561, 567, 577, 588, 612, 621, 675, 693, 768, 833, 867, 891, 943, 972, 1008, 1023, 1083, 1088, 1200, 1204, 1232, 1292, 1323, 1377, 1377
Offset: 1
y=3, x=4, 4^2 + 3^2 = 5^2. 3 is the 1st entry in the list.
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pythtrisq(n) = { local(a,b,c=0,k,x,y,z,vy,j); w = vector(n*n+1); for(a=1,n, for(b=1,n, x=2*a*b; y=b^2-a^2; z=b^2+a^2; if(y > 0 & issquare(x), c++; w[c]=y; print(x","y","z) ) ) ); vy=vector(c); w=vecsort(w); for(j=1,n*n, if(w[j]>0, k++; vy[k]=w[j]; ) ); for(j=1,200, print1(vy[j]",") ) }
A103241
Unreduced numerators of the elements T(n,k)/(n-k)!, read by rows, of the triangular matrix P^-1, which is the inverse of the matrix defined by P(n,k) = (-k^3)^(n-k)/(n-k)! for n >= k >= 1.
Original entry on oeis.org
1, 1, 1, 15, 8, 1, 1024, 368, 27, 1, 198581, 53672, 2727, 64, 1, 85102056, 18417792, 710532, 11904, 125, 1, 68999174203, 12448430408, 386023509, 4975936, 38375, 216, 1, 95264160938080, 14734002979456, 381535651512, 3977848832, 23945000
Offset: 1
Rows of unreduced fractions T(n,k)/(n-k)! begin:
[1/0!],
[1/1!, 1/0!],
[15/2!, 8/1!, 1/0!],
[1024/3!, 368/2!, 27/1!, 1/0!],
[198581/4!, 53672/3!, 2727/2!, 64/1!, 1/0!],
[85102056/5!, 18417792/4!, 710532/3!, 11904/2!, 125/1!, 1/0!], ...
forming the inverse of matrix P where P(n,k) = A103246(n,k)/(n-k)!:
[1/0!],
[-1/1!, 1/0!],
[1/2!, -8/1!, 1/0!],
[-1/3!, 64/2!, -27/1!, 1/0!],
[1/4!, -512/3!, 729/2!, -64/1!, 1/0!], ...
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{T(n,k)=my(P);if(n>=k&k>=1, P=matrix(n,n,r,c,if(r>=c,(-c^3)^(r-c)/(r-c)!))); return(if(n
A103250
Numbers x, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers and y is a perfect square.
Original entry on oeis.org
30, 40, 120, 130, 160, 270, 272, 312, 350, 360, 480, 510, 520, 640, 738, 750, 888, 1000, 1080, 1088, 1160, 1170, 1200, 1218, 1248, 1342, 1400, 1440, 1470, 1920, 1960, 2040, 2080, 2080, 2210, 2430, 2448, 2560, 2590, 2808, 2952, 2968, 3000, 3150, 3240, 3250
Offset: 1
x=30, y=16, 30^2 + 16^2 = 34^2. 30 is the 1st entry in the list.
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pythtrisq(n) = { local(a,b,c=0,k,x,y,z,vy,wx,vx,j); w = vector(n*n+1); for(a=1,n, for(b=1,n, x=2*a*b; y=b^2-a^2; z=b^2+a^2; if(y > 0 & issquare(y), c++; w[c]=x; print(x","y","z) ) ) ); vx=vector(c); w=vecsort(w); for(j=1,n*n, if(w[j]>0, k++; vx[k]=w[j]; ) ); for(j=1,200, print1(vx[j]",") ) }
A103253
Numbers y, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers and z is a perfect square.
Original entry on oeis.org
7, 28, 41, 63, 112, 119, 161, 164, 175, 239, 252, 343, 369, 448, 476, 527, 567, 644, 656, 700, 721, 847, 956, 959, 1008, 1025, 1071, 1081, 1183, 1241, 1372, 1449, 1476, 1519, 1575, 1792, 1904, 2009, 2023, 2047, 2108, 2268, 2527, 2576, 2624, 2800, 2884, 2975
Offset: 1
x=24, y=7, 24^2 + 7^2 = 25^2. 7 is the 1st entry in the list.
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pythtrisq(n) = { local(a,b,c=0,k,x,y,z,vy,wx,vx,vz,j); w = vector(n*n+1); for(a=1,n, for(b=1,n, x=2*a*b; y=b^2-a^2; z=b^2+a^2; if(y > 0 & issquare(z), c++; w[c]=y; print(x","y","z) ) ) ); vy=vector(c); w=vecsort(w); for(j=1,n*n, if(w[j]>0, k++; vy[k]=w[j]; ) ); for(j=1,200, print1(vy[j]",") ) }
Showing 1-6 of 6 results.
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