|
%I #2 Mar 30 2012 17:26:30
%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
|
