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A239135 Numbers k such that (k-1)*k^2 + 1 and k^2 + (k-1) are both prime. 3
2, 3, 5, 6, 8, 13, 21, 24, 26, 28, 35, 45, 48, 50, 55, 76, 83, 89, 93, 96, 100, 101, 115, 120, 138, 140, 148, 149, 181, 191, 195, 203, 206, 209, 215, 230, 258, 259, 281, 285, 294, 301, 309, 323, 330, 349, 358, 373, 380, 386, 393, 395, 423, 428, 433, 474, 495 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers k such that (k^3 - k^2 + 1)*(k^2 + k - 1) is semiprime.

Intersection of A045546 and A111501.

Primes in this sequence: 2, 3, 5, 13, 83, 89, 101, 149, 181, 191, ...

LINKS

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

EXAMPLE

2 is in this sequence because (2-1)*2^2+1=5 and 2^2+(2-1)=5 are both prime.

MATHEMATICA

Select[Range[600], PrimeQ[#^2+#-1]&&PrimeQ[#^2(#-1)+1]&] (* Farideh Firoozbakht, Mar 17 2014 *)

PROG

(MAGMA) k := 1;

     for n in [1..10000] do

        if IsPrime(k*(n - 1)*n^2 + 1) and IsPrime(k*n^2 + n - 1) then

           n;

        end if;

     end for;

CROSSREFS

Cf. A239115.

Sequence in context: A034722 A144712 A050028 * A179791 A139443 A239263

Adjacent sequences:  A239132 A239133 A239134 * A239136 A239137 A239138

KEYWORD

nonn

AUTHOR

Ilya Lopatin following a suggestion from Juri-Stepan Gerasimov, Mar 15 2014

STATUS

approved

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Last modified June 19 03:23 EDT 2021. Contains 345125 sequences. (Running on oeis4.)