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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
81
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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
Let p(i) denote the i-th prime. If 2 p(n) - p(n+1) is a prime, say p(n-i), then we say that p(n) has level(1,i). Sequence gives primes of level(1,1). - 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).
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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
Adjacent sequences: A006559 A006560 A006561 this_sequence A006563 A006564 A006565
Sequence in context: A106097 A163580 A075540 this_sequence A094847 A001992 A139899
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KEYWORD
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nonn,easy,nice
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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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