Voozh

A081945

Numbers k such that both k*(k + 1) + 1 and k*(k - 1) + 1 are primes.

2, 3, 6, 15, 21, 78, 90, 111, 162, 168, 189, 246, 279, 288, 405, 435, 456, 531, 567, 762, 819, 960, 993, 1002, 1092, 1098, 1149, 1182, 1275, 1365, 1422, 1443, 1449, 1548, 1560, 1659, 1701, 1848, 1932, 1974, 2016, 2163, 2205, 2373, 2430, 2451, 2484, 2541

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Numbers k such that k^4 + k^2 + 1 is a semiprime (A001358). - Thomas Ordowski, Sep 24 2015

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

EXAMPLE

6 is a term since both 6*7 + 1 = 43 and 6*5 + 1 = 31 are primes.

MATHEMATICA

Select[Range[3000], PrimeQ[# (# - 1) + 1] && PrimeQ[# (# + 1) + 1] &] (* T. D. Noe, Apr 06 2012 *)

Select[Range[2, 3000], Plus@@Last/@FactorInteger[(#^6 - 1) / (#^2 - 1)] == 2 &] (* Vincenzo Librandi, Sep 24 2015 *)

Select[Range[2600], PrimeOmega[#^4+#^2+1]==2&] (* Harvey P. Dale, Jun 04 2019 *)

PROG

(Magma) [n: n in [0..3000] | IsPrime(n^2+n+1) and IsPrime(n^2-n+1)]; // Vincenzo Librandi, Sep 24 2015

(PARI) for(n=1, 1e3, if (isprime(n*(n+1)+1) && if (isprime(n*(n-1)+1), print1(n", ")))) \\ Altug Alkan, Sep 24 2015

CROSSREFS

Cf. A081944.

Sequence in context: A198684 A293534 A066653 * A329745 A255353 A248652

Adjacent sequences: A081942 A081943 A081944 * A081946 A081947 A081948

KEYWORD

nonn,easy

AUTHOR

Amarnath Murthy, Apr 02 2003

EXTENSIONS

More terms from Don Reble, Apr 08 2003

STATUS

approved

URL: https://oeis.org/A081945

⇱ A081945 - OEIS