

A083771


Rearrangement of primes such that every partial product + 1 is a prime.


7



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

1,1


COMMENTS

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. [Dmitry Kamenetsky, Mar 12 2009]
Records: 2, 3, 5, 7, 11, 19, 29, 59, 67, 97, 113, 233, 251, 587, 881, 953, 1231, 1327, 1553, 1657, 2383, 3251, 3769, 6737, 6947, 7103, 7879, 8263, 10159, 11369, 22003, ..., .  Robert G. Wilson v, Jul 20 2017
Position of the n_th prime: 1, 2, 3, 4, 5, 8, 472, 6, 57, 7, 11, 10, 15, 20, 12, 14, 9, 23, 13, 21, 17, 30, 55, 478, 16, 26, 19, 28, 25, 18, 50, 345, 35, 36, 45, 24, ..., .  Robert G. Wilson v, Jul 20 2017


LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..700 (first 100 terms from Amarnath Murthy and Meenakshi Srikanth)


EXAMPLE

The nth 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. [Dmitry Kamenetsky, Mar 12 2009]


MATHEMATICA

f[s_List] := Block[{p = Times @@ s, q = 2}, While[ MemberQ[s, q]  !PrimeQ[p*q + 1], q = NextPrime@ q]; Append[s, q]]; Nest[f, {2}, 63] (* Robert G. Wilson v, Jul 20 2017 *)


PROG

(PARI) { terms=100; a=A083772=vector(terms); a[1]=2; tmp=1; A083772[1]=3; for(k=2, terms, tmp=tmp*a[k1]; p=1; while(1, until(isprime(p), p=p+2); for(m=1, k1, if(p==a[m], break, if(m==k1, if(isprime(tmp*p+1), a[k]=p; A083772[k]=tmp*p+1; print1(a[k], ", "); break(2))))))); a }


CROSSREFS

Cf. A005235, A039726, A083772.
Cf. number of primality tests required for each term in this sequence is in A158076. [Dmitry Kamenetsky, Mar 12 2009]
Sequence in context: A059878 A105017 A214197 * A158069 A039726 A115617
Adjacent sequences: A083768 A083769 A083770 * A083772 A083773 A083774


KEYWORD

nonn


AUTHOR

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 06 2003


EXTENSIONS

More terms from Rick L. Shepherd, Mar 18 2004


STATUS

approved



