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A083771
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Rearrangement of primes such that every partial product + 1 is a prime.
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4
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2, 3, 5, 7, 11, 19, 29, 13, 59, 37, 31, 47, 67, 53, 41, 97, 73, 113, 103, 43, 71, 233, 61, 151, 109, 101, 251, 107, 587, 79, 223, 167, 311, 239, 137, 139, 359, 181, 257, 337, 163, 173, 881, 563, 149, 409, 157, 179, 293, 127, 331, 191, 269, 317, 83, 277, 23, 821, 373, 271, 283, 461, 569, 853, 487, 433, 647, 953, 383, 199, 367, 1231, 397, 307, 457, 691, 523, 463, 1061, 281, 787, 421, 197, 857, 1103, 347, 631, 499, 991, 643, 769, 983, 607, 811, 449, 1223, 733, 1327, 683, 1021
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OFFSET
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0,1
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COMMENTS
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Though initial terms match it is different from A039726, in that a smaller prime may appear later.
Some of the larger entries may only correspond to probable primes.
A158076 suggests that the numbers in this sequence can be generated quite easily/quickly. Perhaps this sequence is a fast method to generate large probable primes. [From Dmitry Kamenetsky, Mar 12 2009]
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LINKS
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Table of n, a(n) for n=0..99.
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EXAMPLE
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The n-th term is the smallest prime that is not already in the sequence, such that one plus the product of the first n terms is prime. [From Dmitry Kamenetsky, Mar 12 2009]
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PROG
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(PARI) { terms=100; a=A083772=vector(terms); a[1]=2; tmp=1; A083772[1]=3; for(k=2, terms, tmp=tmp*a[k-1]; p=1; while(1, until(isprime(p), p=p+2); for(m=1, k-1, if(p==a[m], break, if(m==k-1, if(isprime(tmp*p+1), a[k]=p; A083772[k]=tmp*p+1; print1(a[k], ", "); break(2))))))); a }
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CROSSREFS
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Cf. A039726, A083772.
Cf. number of primality tests required for each term in this sequence is in A158076. [From Dmitry Kamenetsky, Mar 12 2009]
Sequence in context: A059878 A105017 A214197 * A158069 A039726 A115617
Adjacent sequences: A083768 A083769 A083770 * A083772 A083773 A083774
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 06 2003
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EXTENSIONS
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More terms from Rick L. Shepherd, Mar 18 2004
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STATUS
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approved
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