A159190
Main diagonal of array mentioned in A113941.
Original entry on oeis.org
6, 9, 1247, 1891, 29539
Offset: 1
The array begins:
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....|.n=1.|.n=2.|.n=3.|..n=4.|..n=5.|in OEIS.|
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k=3.|...6.|..10.|...15.|...21.|....253.|A113940
k=4.|...4.|...9.|...25.|...49.|....121.|A001248
k=5.|..35.|.247.|.1247.|..2501.|..4187.|A113941
k=6.|...6.|..15.|..703.|..1891.|..2701.|new
k=7.|.403.|.697.|.2059.|.25351.|.29539.|new
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A255584
Semiprimes of the form (4*n + 1)*(6*n + 1) = 24*n^2 + 10*n + 1.
Original entry on oeis.org
35, 247, 1247, 2501, 4187, 7957, 15251, 17767, 33227, 49051, 81317, 118301, 128627, 182527, 241001, 250717, 265651, 302177, 318551, 438751, 485357, 563347, 655051, 679057, 736751, 753667, 886657, 981317, 1010651, 1090987, 1163801, 1361837, 1563151
Offset: 1
35 is in the sequence because 35 = 5*7 and 5, 7 are primes of the form 4*k+1 and 6*k+1 respectively.
247 is in the sequence because 247 = 13*19: both 13, 19 are primes of the form 6*k+1 and 13 also has the form 4*k+1.
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[(4*n+1)*(6*n+1): n in [1..300] | IsPrime(4*n+1) and IsPrime(6*n+1)];
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IsSemiprime:=func; [s: n in [1..300] | IsSemiprime(s) where s is 24*n^2+10*n+1];
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Select[Table[24 n^2 + 10 n + 1, {n, 300}], PrimeOmega[#] == 2 &] (* or *) f[n_] := Last /@ FactorInteger[n] == {1, 1}; Select[Array[24 #^2 + 10 # + 1 &, 300], f[#] &]
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for(n=1,250,if(bigomega(s=24*n^2+10*n+1)==2,print1(s,", "))) \\ Derek Orr, Feb 28 2015
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