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A095672
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Primes p = p_(n+1) such that p_n + p_(n+2) = 2*p_(n+1) + 4.
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8
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31, 61, 73, 151, 271, 293, 337, 401, 433, 491, 547, 571, 577, 601, 743, 761, 839, 911, 1033, 1039, 1063, 1201, 1231, 1291, 1321, 1409, 1453, 1531, 1571, 1621, 1627, 2003, 2017, 2039, 2131, 2243, 2273, 2341, 2383, 2551, 2663, 2713, 2719, 2791, 3041, 3049
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OFFSET
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1,1
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COMMENTS
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Primes that are first prime chords.
These come from music based on the prime differences where the chords are an even number of note steps from the primary note.
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LINKS
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EXAMPLE
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31 is a term because 29+37 = 2*31 + 4 = 66.
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MAPLE
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primes:= select(isprime, [seq(i, i=3..10000, 2)]):
L:= primes[1..-3]+primes[3..-1]-2*primes[2..-2]:
primes[select(t -> L[t-1]=4, [$2..nops(L)+1])]; # Robert Israel, Jun 28 2018
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MATHEMATICA
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m = 1; Prime[1 + Select[ Range[450], Prime[ # + 2] - 2*Prime[ # + 1] + Prime[ # ] - 4*m == 0 &]] (* Robert G. Wilson v, Jul 14 2004 *)
Select[Partition[Prime[Range[500]], 3, 1], #[[1]]+#[[3]]==2#[[2]]+4&][[;; , 2]] (* Harvey P. Dale, Jan 31 2024 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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