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A071580 Smallest prime of the form k*a(n-1)*a(n-2)*...*a(1)+1. 4
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.

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 * A267507 A344561 A014546

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 December 10 02:09 EST 2022. Contains 358712 sequences. (Running on oeis4.)