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Search: id:A090120
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| A090120 |
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Numbers x such that x^2 is such that nextprime[x^2]-prevprim[x^2]=4. |
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2
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| 3, 4, 9, 10, 14, 15, 20, 21, 26, 33, 40, 110, 117, 124, 146, 206, 237, 250, 273, 303, 309, 326, 340, 350, 387, 429, 436, 440, 441, 447, 470, 513, 561, 573, 609, 634, 686, 704, 807, 897, 920, 1004, 1035, 1054, 1060, 1071, 1113, 1124, 1143, 1156, 1233, 1239
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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Solutions to {x; A007918[x^2]-A007917[x^2]=4}.
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EXAMPLE
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n=3, n^2=9, p is surrounded by closest primes: {7,[9],11};
n=10, n^2=100 is surrounded by {97,[100],101};
remark that the gap=4 is partitioned either as 2+2 or
as 3+1; 1+3 never occurs since n^2-1 is composite if n>2.
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MATHEMATICA
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pre[x_] := Prime[PrimePi[x]] nex[x_] := Prime[PrimePi[x]+1] de[x_] := Prime[PrimePi[x]+1]-Prime[PrimePi[x]] Do[s=de[n^2]; If[Equal[s, 4], Print[{pre[n^2], n^2, nex[n^2], n}]], {n, 2, 200}]
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CROSSREFS
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Cf. A090116-A090119, A007917, A007918, A000720, A000040, A053001, A007491, A000290.
Sequence in context: A121153 A059985 A137709 this_sequence A129783 A093513 A047230
Adjacent sequences: A090117 A090118 A090119 this_sequence A090121 A090122 A090123
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jan 09 2004
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