

A255584


Semiprimes of the form (4*n + 1)*(6*n + 1) = 24*n^2 + 10*n + 1.


5



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
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OFFSET

1,1


COMMENTS

The first few values of n such that both n and n+1 give semiprimes in the sequence begin: 2607, 4017, 4062, 5967, 7107, 8472, 8892, ... In such cases, numbers of the form 10n+8 can always be expressed as the sum of the two primes 4n+1 and 6n+7.  Wesley Ivan Hurt, Feb 27 2015


LINKS



FORMULA



EXAMPLE

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.


MATHEMATICA

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[#] &]


PROG

(Magma) [(4*n+1)*(6*n+1): n in [1..300]  IsPrime(4*n+1) and IsPrime(6*n+1)]; /* or */ IsSemiprime:=func<n  &+[d[2]: d in Factorization(n)] eq 2>; [s: n in [1..300]  IsSemiprime(s) where s is 24*n^2+10*n+1];
(PARI) for(n=1, 250, if(bigomega(s=24*n^2+10*n+1)==2, print1(s, ", "))) \\ Derek Orr, Feb 28 2015


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



