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A285486 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. 1
1, 1, 1, 1, 5, 1, 1, 1, 13, 11, 1, 5, 5, 7, 1, 1, 1, 5, 7, 1, 1, 11, 1, 7, 5, 7, 1, 1, 23, 1, 11, 1, 19, 5, 13, 1, 1, 1, 5, 5, 5, 29, 19, 1, 1, 5, 1, 1, 37, 5, 5, 17, 11, 13, 25, 13, 5, 41, 7, 1, 5, 1, 25, 7, 5, 7, 1, 1, 5, 11, 11, 5, 5, 5, 5, 11, 5, 1, 11, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

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.

LINKS

Lei Zhou, Table of n, a(n) for n = 1..10000

EXAMPLE

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

In the similar way, 1*A007694(2) + 1 = 1*2 + 1 = 3 is the first prime number found for n = 2, so a(2) = 1.

...

For n = 5, A007694(5) = 8, 5*8 + 1 = 41 is the smallest prime found, so a(5) = 5.

MATHEMATICA

b = 2; a = {1, b}; sp = {1}; r = {b}; While[Length[sp] < 79, f = 0;

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

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

  AppendTo[sp, 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]]]; sp

CROSSREFS

Cf. A003586, A007310, A007694, A285483.

Sequence in context: A145295 A091051 A183097 * A230368 A256690 A181985

Adjacent sequences:  A285483 A285484 A285485 * A285487 A285488 A285489

KEYWORD

nonn,easy

AUTHOR

Lei Zhou, Apr 19 2017

STATUS

approved

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Last modified June 24 21:16 EDT 2019. Contains 324337 sequences. (Running on oeis4.)