The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A046869 Good primes (version 1): prime(n)^2 > prime(n-1)*prime(n+1). 12
 5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 157, 163, 173, 179, 191, 197, 211, 223, 227, 239, 251, 257, 263, 269, 277, 281, 307, 311, 331, 347, 367, 373, 379, 397, 419, 431, 439, 457, 461, 479, 487, 499, 521, 541 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also called geometrically strong primes. - Amarnath Murthy, Mar 08 2002 The idea can be extended by defining a geometrically strong prime of order k to be a prime that is greater than the geometric mean of r neighbors on both sides for all r = 1 to k but not for r = k+1. Similar generalizations can be applied to the sequence A051634. - Amarnath Murthy, Mar 08 2002 It appears that a(n) ~ 2*prime(n). - Thomas Ordowski, Jul 25 2012 Conjecture: primes p(n) such that 2*p(n) >= p(n-1) + p(n+1). - Thomas Ordowski, Jul 25 2012 Probably {3,7,23} U {good primes} = {primes p(n) > 2/(1/p(n-1) + 1/p(n+1))}. - Thomas Ordowski, Jul 27 2012 Except for A001359(1), A001359 is a subsequence. - Chai Wah Wu, Sep 10 2019 REFERENCES R. K. Guy, Unsolved Problems in Number Theory, Section A14. LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 EXAMPLE 37 is a member as 37^2 = 1369 > 31*41 = 1271. MAPLE with(numtheory): a := [ ]: P := [ ]: M := 300: for i from 2 to M do if p(i)^2>p(i-1)*p(i+1) then a := [ op(a), i ]; P := [ op(P), p(i) ]; fi; od: a; P; MATHEMATICA Do[ If[ Prime[n]^2 > Prime[n - 1]*Prime[n + 1], Print[ Prime[n] ] ], {n, 2, 100} ] Transpose[Select[Partition[Prime[Range], 3, 1], #[]^2>#[]#[]&]][] (* Harvey P. Dale, May 13 2012 *) Select[Prime[Range[2, 100]], #^2 > NextPrime[#]*NextPrime[#, -1] &] (* Jayanta Basu, Jun 29 2013 *) PROG (PARI) forprime(n=o=p=3, 999, o+0<(o=p)^2/(p=n) & print1(o", ")) isA046869(p)={ isprime(p) & p^2>precprime(p-1)*nextprime(p+1) } \\ M. F. Hasler, Jun 15 2011 (Magma) [NthPrime(n): n in [2..100] | NthPrime(n)^2 gt NthPrime(n-1)*NthPrime(n+1)]; // Bruno Berselli, Oct 23 2012 CROSSREFS Cf. A001359, A006562, A028388, A046868, A051634, A051635, A068828. Sequence in context: A023489 A268307 A108294 * A028388 A277718 A067606 Adjacent sequences:  A046866 A046867 A046868 * A046870 A046871 A046872 KEYWORD nonn AUTHOR EXTENSIONS Corrected and extended by Robert G. Wilson v, Dec 06 2000 Edited by N. J. A. Sloane at the suggestion of Giovanni Resta, Aug 20 2007 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 26 20:57 EDT 2022. Contains 357050 sequences. (Running on oeis4.)