The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A098845 Numbers k such that 4^k - 2^k - 1 is prime. 10
 2, 4, 5, 9, 10, 18, 38, 45, 50, 57, 108, 161, 208, 224, 225, 240, 354, 597, 634, 1008, 1080, 1468, 1525, 1560, 3298, 3329, 3846, 4129, 5430, 8616, 11834, 12988, 14610, 43401, 45306, 53776, 54449, 67497, 74025, 122449, 136845, 142896, 164541, 171157, 187668, 274054, 316944, 349296 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All primes certified using PFGW from primeform group. - Pierre CAMI, Mar 07 2005 No terms 2, 3, 7, 12, 13 or 15 (mod 20) except 2. - Robert Israel, Dec 08 2015, updated by Fabrice Lavier, Jan 10 2019 Using such "Goldilocks" primes (a term coined by Mike Hamburg) as modulus facilitates use of Karatsuba multiplication in elliptic-curve cryptography. - Francois R. Grieu, Mar 25 2021 LINKS Table of n, a(n) for n=1..48. Chris Caldwell, The largest known primes Mike Hamburg, Ed448-Goldilocks, a new elliptic curve, Cryptology ePrint Archive, Report 2015/625. MAPLE select(t -> isprime(4^t-2^t-1), [\$1..1000]); # Robert Israel, Dec 08 2015 MATHEMATICA Select[Range[15000], PrimeQ[4^# - 2^# - 1] &] (* Vincenzo Librandi, Dec 08 2015 *) PROG (Magma) [n: n in [0..1000] | IsPrime(2^n*(2^n-1)-1)]; // Vincenzo Librandi, Dec 08 2015 (PARI) for(n=1, 1e3, if(ispseudoprime(4^n-2^n-1), print1(n, ", "))) \\ Altug Alkan, Dec 08 2015 (Python) from sympy import isprime for n in range(1, 1000): if isprime(4**n-2**n-1): print(n, end=', ') # Stefano Spezia, Jan 11 2019 CROSSREFS Cf. similar sequences listed in A265481. Sequence in context: A319423 A265748 A191001 * A298981 A069001 A287181 Adjacent sequences: A098842 A098843 A098844 * A098846 A098847 A098848 KEYWORD nonn AUTHOR Pierre CAMI, Oct 10 2004; extended several times: Jun 01 2005, Jun 19 2006, May 03 2007 EXTENSIONS Extended to a(44) = 349296 (2^698592 - 2^349296 - 1 is a 210298-digit certified prime) by Pierre CAMI, Jan 11 2009 Definition simplified by Pierre CAMI, May 10 2012 a(30) corrected by Robert Israel, Dec 14 2015 4 missing terms between a(41) = 136845 and what is now a(46) = 274054 added by Fabrice Lavier, Jan 10 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 19 18:58 EDT 2024. Contains 373507 sequences. (Running on oeis4.)