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A279052 Semiprimes whose binary and ternary representations are prime when read in decimal. 1


%S 295,1189,2515,4399,4897,5137,7045,7261,7999,8065,9019,9637,10579,

%T 10951,10963,11035,11233,12679,13315,13603,13849,16279,18295,20065,

%U 20467,20497,23089,23419,23551,23983,26359,27007,27301,27787,29647,33127,33253,33763,34189,34411

%N Semiprimes whose binary and ternary representations are prime when read in decimal.

%H K. D. Bajpai and Charles R Greathouse IV, <a href="/A279052/b279052.txt">Table of n, a(n) for n = 1..10000</a> (first 4075 terms from K. D. Bajpai)

%e 295 is in the sequence because 295 = 5*59 (semiprime), 295_10 = 100100111_2 = 101221_3, and both 100100111_10 and 101221_10 are prime.

%e 1189 is in the sequence because 1189 = 29*41 (semiprime), and both its binary representation 10010100101 and its ternary representation 1122001, if read as decimal numbers, are prime.

%t Select[Range[50000], PrimeOmega[#] == 2 && PrimeQ[FromDigits[IntegerDigits[#, 2]]] && PrimeQ[FromDigits[IntegerDigits[#, 3]]] &]

%o (PARI) has(n,b)=isprime(fromdigits(digits(n,b),10))

%o list(lim)=my(v=List(),t); forprime(p=2,lim\2, forprime(q=2,min(lim\p,p), if(has(t=p*q,2) && has(t,3), listput(v,t)))); Set(v) \\ _Charles R Greathouse IV_, Dec 05 2016

%Y Subsequence of A001358.

%Y Cf. A000040, A007089, A036952, A065720, A236365, A236537.

%K nonn,base

%O 1,1

%A _K. D. Bajpai_, Dec 05 2016

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Last modified December 5 20:38 EST 2019. Contains 329777 sequences. (Running on oeis4.)