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A231207
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The primes given as concatenation of chunks of A231206 whose lengths (in number of terms) are given by the terms of A231206.
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2
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23, 149, 5, 67819, 1011121314151617139, 1820212259, 232425262763, 28293031323371, 3435363738394057, 414243444546474849505152535455565860109, 616264656667686970189, 72737475767778798081179, 8283848586878889909192173
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OFFSET
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1,1
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COMMENTS
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The n-th term is the concatenation of (the "next") A231206(n) terms of A231206.
The last term of A231206 used to produce the n-th prime is usually roughly twice as large as its neighbors, see example. This in turn leads to primes about twice as long as their neighbors in this sequence.
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LINKS
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EXAMPLE
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Concatenation of the first A231206(1)=2 terms of A231206 yields the first prime a(1)=23. Concatenation of the next A231206(2)=3 terms of A231206 yields a(2)=149.
The terms of A231206 in which ends the primes a(n) are usually roughly twice as large as their neighbors: ... 4, 9, 5,... 9, 19, 10,... 25, 59, 26,... 27, 63, 28,... 33, 71, 34,... 60, 109, 61,... 70, 198, 72,... 81, 179, 82,... But to make the 5th prime, the term A231206(19)=139 had to be chosen much larger than its neighbors (17 and 18), which in turn leads to the 417 digit prime a(19), concatenation of A231206(173..311). To get this prime, one has to take A231206(311)=581 roughly twice as large as his neighbors A231206(310)=309 and A231206(312)=310. This leads later again to a prime roughly twice as long as its neighbors in this sequence.
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PROG
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(PARI) {a=[prefix=2]; remain=pointer=1; for(n=1, 499, my(used=Set(a)); if( !remain, remain=a[pointer++]; print1(prefix", "); prefix=""); for(i=1, 1e9, setsearch(used, i) && next; remain>1 || ispseudoprime( eval( Str( prefix, i ))) || next; prefix=Str(prefix, i); a=concat(a, i); remain--; break ))}
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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