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A270190
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Numbers n for which prime(n+1)-prime(n) is a multiple of three.
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12
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9, 11, 15, 16, 18, 21, 23, 32, 36, 37, 39, 40, 46, 47, 51, 54, 55, 56, 58, 67, 71, 73, 74, 76, 84, 86, 91, 96, 97, 99, 100, 102, 103, 105, 107, 108, 110, 111, 114, 118, 119, 121, 123, 129, 130, 133, 139, 160, 161, 164, 165, 167, 168, 170, 174, 179, 180, 184, 185, 187, 188, 194, 195, 197, 199, 200, 202, 203, 205, 208, 210
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OFFSET
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1,1
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COMMENTS
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Numbers n for which A001223(n) = 0 modulo 3.
Equivalently, numbers n for which prime(n+1)-prime(n) is a multiple of six. See A276414 for runs of increasing length of consecutive integers. - M. F. Hasler, Sep 03 2016
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LINKS
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FORMULA
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Other identities. For all n >= 1:
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EXAMPLE
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9 is present as the difference between A000040(9+1) = 29 and A000040(9) = 23 is 6, a multiple of three.
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MATHEMATICA
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Select[Range@ 210, Divisible[Prime[# + 1] - Prime@ #, 3] &] (* Michael De Vlieger, Mar 17 2016 *)
PrimePi/@Select[Partition[Prime[Range[350]], 2, 1], Divisible[#[[2]]-#[[1]], 3]&][[All, 1]] (* Harvey P. Dale, Jul 11 2017 *)
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PROG
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(PARI) isok(n) = ((prime(n+1) - prime(n)) % 3) == 0; \\ Michel Marcus, Mar 17 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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