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A046869
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Good primes (version 1): p(n)^2 > p(n-1)*p(n+1).
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11
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| Also called geometrically strong primes. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), 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 (amarnath_murthy(AT)yahoo.com), Mar 08 2002
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REFERENCES
| R. K. Guy, Unsolved Problems in Number Theory, Section A14.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
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EXAMPLE
| 37 is a member as 37^2 = 1369 > 31*41= 1271.
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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;
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MATHEMATICA
| Do[ If[ Prime[n]^2 > Prime[n - 1]*Prime[n + 1], Print[ Prime[n] ] ], {n, 2, 100} ]
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PROG
| Contribution by M. F. Hasler, Jun 15 2011 (Start)
(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) }
(End)
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CROSSREFS
| Cf. A068828, A051634, A051635, A006562, A046868, A028388.
Sequence in context: A089110 A023489 A108294 * A028388 A067606 A184247
Adjacent sequences: A046866 A046867 A046868 * A046870 A046871 A046872
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 06 2000
Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Giovanni Resta, Aug 20 2007
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