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Search: id:A114961
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| A114961 |
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Numbers n such that PrimePi(prime(n + 1)^2) - PrimePi(prime(n)^2) < c*n with c=9/5. |
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1
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| 7, 10, 13, 20, 26, 28, 33, 35, 43, 45, 49, 52, 57, 60, 64, 89, 98, 109, 113, 116, 120, 140, 142, 144, 148, 152, 171, 173, 176, 178, 182, 190, 201, 209, 212, 215, 225, 230, 234, 236, 253, 256, 262, 265, 268, 277, 286, 288, 294, 296, 302, 307, 313, 315, 318, 320
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If c=2 instead of 1.8 then the sequence is A029707.
This sequence is probably finite with 699 terms with 14020 being the last.
If c=1.7 the sequence is just {7, 10, 13, 20, 26, 28, 33, 35, 45, 49, 57, 60, 64, 89, 98, 109, 113, 116, 171, 190, 201, 215, 225, 234, 236, 256, 288, 332, 384, 405, 430, 486, 495, 498, 524, 530, 601, 613, 625, 872}.
If c=1.6 the sequence is just {7, 13, 20, 28, 33, 57, 109}.
If c=3/2 the sequence has but one term, 33.
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REFERENCES
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P. Ribenboim, The New Book of Prime Number Records, Springer-Verlag, NY, 1995, page 248.
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MATHEMATICA
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t = {}; Do[ If[ PrimePi[ Prime[n + 1]^2] - PrimePi[ Prime[n]^2] < 9n/5, AppendTo[t, n]], {n, 10^5}]; t
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CROSSREFS
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Cf. A029707.
Adjacent sequences: A114958 A114959 A114960 this_sequence A114962 A114963 A114964
Sequence in context: A026319 A120153 A007770 this_sequence A123834 A064629 A059752
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 21 2006
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