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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..33.

FORMULA

a(n) = A033570(A130800(n)) = A033570(2*A255607(n)). - M. F. Hasler, Dec 13 2019

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

Subsequence of A245365.

Cf. A001358, A002144, A002476, A113941, A255607 (associated n).

Equals A033570(A130800). - M. F. Hasler, Dec 13 2019

Sequence in context: A219474 A220208 A068722 * A113941 A067238 A267022

Adjacent sequences:  A255581 A255582 A255583 * A255585 A255586 A255587

KEYWORD

nonn

AUTHOR

Vincenzo Librandi, Feb 27 2015

STATUS

approved

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Last modified March 29 05:39 EDT 2020. Contains 333105 sequences. (Running on oeis4.)