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A168513 Number of 2n-digit primes that are concatenation of n two-digit distinct primes p_1...p_n, 98>p_1>p_2>...>p_n>10. 2

%I

%S 21,36,300,722,2493,4766,9459,13091,18484,18779,18048,12995,9122,4424,

%T 2160,639,234,48,8,0,0

%N Number of 2n-digit primes that are concatenation of n two-digit distinct primes p_1...p_n, 98>p_1>p_2>...>p_n>10.

%C There are 21 two-digit primes, hence n=1..21, and a(1)=21.

%C Also a(2)=36, see A168499, and a(3)=300, see A168500;

%C a(20)=0 because among 21 twenty-digit numbers no one is prime;

%C a(21)=0 because the only possible 42-digit number is composite:

%C 978983797371676159534743413731292319171311=

%C 2633*561934423224622169*661666288057389220943.

%t pr2={97,89,83,79,73,71,67,61,59,53,47,43,41,37,31,29,23,19,17,13,11};

%t Table[ssk=Subsets[pr2,{k}];Le=Binomial[21,k];c=0;

%t Do[If[PrimeQ[fd=FromDigits[Flatten[IntegerDigits/@ssk[[i]]]]],c++ ],{i,Le}];{k,c},{k,21}]

%t {1,21},{2,36},{3,300},{4,722},{5,2493},{6,4766},{7,9459},{8,13091},

%t {9,18484},{10,18779},{11,18048},{12,12995},{13,9122},{14,4424},

%t {15,2160},{16,639},{17,234},{18,48},{19,8},{20,0},{21,0}.

%Y Cf. A168499, A168500.

%K base,fini,full,nonn

%O 1,1

%A _Zak Seidov_, Nov 28 2009

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Last modified October 24 15:56 EDT 2021. Contains 348233 sequences. (Running on oeis4.)