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 A071580 Smallest prime of the form k*a(n-1)*a(n-2)*...*a(1)+1. 5
 2, 3, 7, 43, 3613, 65250781, 5109197227031017, 21753246920584523633819544186061, 993727878334632126576336773629979379563850938567846991629270287 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The former definition was "Smallest prime == 1 mod (a(n-1)*a(n-2)*...*a(1)) for n>=2 with a(1)=2." a(6) through a(13), with digit lengths 8, 16, 32, 63, 127, 253, 507 and 1012, respectively, have been certified prime with Primo. There is no need to use Elliptic curve primality proving (ECPP) to certify the primes. The primality of each term can be proved recursively with the "N-1 method" since the full factorization of a(n)-1 is known. - Jeppe Stig Nielsen, May 14 2023 LINKS Joerg Arndt, Table of n, a(n) for n = 1..13 Mersenne Forum, A071580 MAPLE P:= 1: for n from 1 to 13 do for k from 1 do if isprime(k*P+1) then A[n]:= k*P+1; P:= P * A[n]; break fi od od: seq(A[i], i=1..13); # Robert Israel, May 19 2015 MATHEMATICA sp[{p_, a_}]:=Module[{k=1}, While[!PrimeQ[k*p+1], k++]; {p(p*k+1), p*k+1}]; NestList[sp, {2, 2}, 10][[All, 2]] (* Harvey P. Dale, Mar 04 2019 *) PROG (PARI) terms=13; v=vector(terms); p=2; v[1]=p; for(n=2, terms, q=p+1; while(!isprime(q), q=q+p); v[n]=q; p=p*q); v CROSSREFS Cf. A061092, A258081. Sequence in context: A129871 A075442 A082993 * A359340 A267507 A344561 Adjacent sequences: A071577 A071578 A071579 * A071581 A071582 A071583 KEYWORD nonn AUTHOR Rick L. Shepherd, May 31 2002 EXTENSIONS Definition reworded by Andrew R. Booker, May 19 2015 STATUS approved

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Last modified April 20 06:53 EDT 2024. Contains 371799 sequences. (Running on oeis4.)