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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A234798 Numbers k such that (k^i)+7 for 1<=i<=7 are seven prime numbers. 1
 0, 3981186, 146202480, 1165139284, 2002776304, 5677052574, 9441118506, 13199287564, 14655461200, 21663769144, 23911959136, 28132616434, 29959257966, 34716681516, 35619315204, 35690387094, 38966503234, 42887165056, 45425679640, 47063988520, 51444908350, 53558122980 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture: the sequence is infinite. LINKS Table of n, a(n) for n=1..22. EXAMPLE 0 is in the sequence since (0^i)+7 = 7 is prime for i>0. 3981186 is in the sequence because the following seven numbers are primes: 3981186+7, 3981186^2+7, ..., 3981186^7+7. PROG (Java) import java.math.*; public class A234798 { public static void main (String[] args) { BigInteger c7 = BigInteger.valueOf(7); for (long i=0; ; i+=2) { if (!BigInteger.valueOf(i+7).isProbablePrime(80)) continue; BigInteger bi = BigInteger.valueOf(i), b=bi; long k; for (k=1; k<7; ++k) { b = b.multiply(bi); if (!b.add(c7).isProbablePrime(80)) break; } if (k==7) System.out.printf("%d, ", i); } } } CROSSREFS Cf. A000040. Sequence in context: A144642 A032753 A047987 * A290123 A146946 A109207 Adjacent sequences: A234795 A234796 A234797 * A234799 A234800 A234801 KEYWORD nonn,hard AUTHOR Alex Ratushnyak, Dec 30 2013 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 September 8 01:34 EDT 2024. Contains 375749 sequences. (Running on oeis4.)