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A285483 a(n) is the smallest positive integer that makes a(n)*A007694(n)-1 a prime number, while a(n) and A007694(n) are coprimes. 2
7, 1, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 17, 1, 5, 1, 1, 5, 5, 1, 7, 5, 5, 5, 1, 1, 13, 7, 5, 1, 11, 1, 1, 5, 1, 17, 19, 17, 19, 5, 25, 5, 1, 7, 5, 13, 11, 5, 1, 5, 5, 7, 1, 1, 19, 1, 1, 17, 5, 7, 29, 1, 5, 1, 5, 7, 7, 17, 1, 7, 7, 1, 7, 49, 5, 13, 13, 25, 5, 5, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

All terms are elements of A007310, which are free of prime factor 2 and 3, since if a(n) has a factor of 2, 2*A007694(n) is also an element of A007694. Ditto for a(n) is divisible by 3 cases.

a(1) is not defined since any odd number greater than 3 minus 1 is an even nonprime number.

LINKS

Lei Zhou, Table of n, a(n) for n = 2..10001

EXAMPLE

For n = 2, A007694(2) = 2, testing k*2-1 for k in set {1, 5, 7, 11, 13, 17, 19... }, we find that 7*2 - 1 = 13 is the first prime number found.  So a(2) = 7;

In the similar way, 1*A007694(3) - 1 = 1*4 - 1 = 3 is the first prime number found for n = 3, so a(3) = 1.

For n = 7, A007694(7) = 16, 5*16 - 1 = 89 is the smallest prime found, so a(7) = 5.

MATHEMATICA

b = 2; a = {b}; sm = {}; r = a; While[Length[sm] < 81, f = 0;

While[f++; (fc = FactorInteger[f];

    MemberQ[{2, 3}, fc[[1, 1]]]) || (! PrimeQ[f*a[[Length[a]]] - 1])];

  AppendTo[sm, f]; c = r*2; d = r*3; e = Sort[Union[c, d]]; i = 1;

While[e[[i]] <= a[[Length[a]]], i++]; AppendTo[a, e[[i]]];

AppendTo[r, e[[i]]];

While[(3*r[[1]]) < r[[Length[r]]], r = Delete[r, 1]]]; sm

CROSSREFS

Cf. A003586, A007310, A007694.

Sequence in context: A248909 A140213 A331927 * A284097 A091258 A174544

Adjacent sequences:  A285480 A285481 A285482 * A285484 A285485 A285486

KEYWORD

nonn,easy

AUTHOR

Lei Zhou, Apr 19 2017

STATUS

approved

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Last modified July 29 17:41 EDT 2021. Contains 346346 sequences. (Running on oeis4.)