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A022884
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Numbers k such that prime(k) + prime(k+3) = prime(k+1) + prime(k+2).
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4
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3, 4, 5, 6, 9, 12, 16, 21, 25, 26, 27, 29, 33, 37, 41, 43, 48, 54, 56, 63, 71, 74, 77, 80, 81, 84, 88, 92, 93, 100, 103, 105, 108, 124, 125, 126, 134, 140, 142, 147, 149, 151, 153, 156, 165, 171, 175, 176, 181, 185, 191, 200, 208, 211, 216, 224, 234, 235
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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The ninth prime is 23. We verify that 23 + 37 = 60 = 29 + 31. Hence 9 is in the sequence.
The tenth prime is 29. We see that 29 + 41 = 70 but 31 + 37 = 68, so 10 is not in the sequence.
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MATHEMATICA
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Select[Range@ 240, Prime[#] + Prime[# + 3] == Prime[# + 1] + Prime[# + 2] &] (* Michael De Vlieger, Oct 28 2015 *)
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PROG
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(PARI) isok(k) = prime(k+3)+prime(k) == prime(k+1)+prime(k+2); \\ Michel Marcus, Aug 20 2015
(PARI) is(n, p=prime(n))=my(q=nextprime(p+1), r=nextprime(q+1), s=nextprime(r+1)); p+s==q+r
(Magma) [n: n in [1..250] |(NthPrime(n)+NthPrime(n+3)) eq (NthPrime(n+1)+ NthPrime(n+2))]; // Vincenzo Librandi, Nov 04 2018
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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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