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Search: id:A006562
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| A006562 |
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Balanced primes (of order one): primes which are the average of the previous prime and the following prime.
(Formerly M4011)
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+0
80
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| 5, 53, 157, 173, 211, 257, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103, 1123, 1187, 1223, 1367, 1511, 1747, 1753, 1907, 2287, 2417, 2677, 2903, 2963, 3307, 3313, 3637, 3733, 4013, 4409, 4457, 4597, 4657, 4691, 4993, 5107, 5113, 5303, 5387, 5393
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Subsequence of A075540. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 11 2006
This subsequence of A125830 and of A162174 gives primes of level (1,1): More generally, the i-th prime p(i) is of level (1,k) iff it has level 1 in A117563 and 2 p(i) - p(i+1) = p(i-k). - Remi Eismann (reismann(AT)free.fr), Feb 15 2007
Note the similarity between plots of A006562 and A013916 [From Bill McEachen (bmceache(AT)centralsan.org), Sep 07 2009]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.
A. Murthy, Smarandache Notions Journal, Vol. 11 N. 1-2-3 Spring 2000.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Rev. ed. 1997), p. 134
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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FORMULA
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2*p_n = p_(n-1) + p_(n+1).
A006562 = { p = prime(k) | A118534(k) = prime(k-1) }. [From R. Eismann, Nov 30 2009]
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EXAMPLE
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5 belongs to the sequence because 5 = (3 + 7)/2. Likewise 53 = (47 + 59)/2.
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MATHEMATICA
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Transpose[ Select[ Partition[ Prime[ Range[1000]], 3, 1], #[[2]] ==(#[[1]] + #[[3]])/2 &]][[2]]
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PROGRAM
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(PARI) betwixtpr(n) = { local(c1, c2, x, y); for(x=2, n, c1=c2=0; for(y=prime(x-1)+1, prime(x)-1, if(!isprime(y), c1++); ); for(y=prime(x)+1, prime(x+1)-1, if(!isprime(y), c2++); ); if(c1==c2, print1(prime(x)", ")) ) } - Cino Hilliard (hillcino368(AT)gmail.com), Jan 25 2005
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CROSSREFS
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Cf. A082077, A082078, A082079, A096697, A096698, A096699, A096700, A096701, A096702, A096703, A096704.
Cf. A096693, A051634, A051635, A054342.
Cf. A117078, A117563, A125830, A006562, A117876, A125576
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KEYWORD
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nonn,easy,nice,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com) and Robert G. Wilson v
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EXTENSIONS
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Reworded comment and added formula from R. Eismann M. F. Hasler (mhasler(AT)univ-ag.fr), Nov 30 2009
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