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A358530
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a(n) = n-th prime p(k) such that p(k) - p(k-1) < p(k-1) - p(k-2).
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5
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13, 19, 31, 41, 43, 61, 71, 73, 83, 101, 103, 109, 131, 139, 151, 167, 181, 193, 199, 227, 229, 241, 257, 271, 281, 283, 311, 313, 337, 349, 373, 383, 401, 421, 433, 443, 461, 463, 487, 491, 503, 523, 547, 563, 571, 593, 601, 617, 619, 641, 643, 661, 677
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OFFSET
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1,1
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COMMENTS
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This sequence, together with A358528 and A181424, partition the set of primes >= 5. The corresponding sequences of indices, A358531, A358529, and A356347, partition the set of positive integers >= 3.
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LINKS
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Table of n, a(n) for n=1..53.
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FORMULA
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a(n) = A051634(n) + 2.
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EXAMPLE
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n 1 2 3 4 5 6 7
k 6 8 11 13 14 18 20
p(n) 13 19 31 41 43 61 71
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MATHEMATICA
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t = Select[2 + Range[140],
Prime[#] - Prime[# - 1] < Prime[# - 1] - Prime[# - 2] &] (* A358531 *)
Prime[t] (* A358530 *)
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CROSSREFS
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Cf. A001223, A051634, A079419, A358528, A358529, A358531, A181424, A356347.
Sequence in context: A085413 A342943 A244311 * A164333 A182365 A069324
Adjacent sequences: A358527 A358528 A358529 * A358531 A358532 A358533
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling, Nov 21 2022
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STATUS
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approved
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