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Search: id:A114537
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| A114537 |
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Dispersion of the primes (an array read by antidiagonals). |
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+0
4
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| 1, 2, 4, 3, 7, 6, 5, 17, 13, 8, 11, 59, 41, 19, 9, 31, 277, 179, 67, 23, 10, 127, 1787, 1063, 331, 83, 29, 12, 709, 15299, 8527, 2221, 431, 109, 37, 14, 5381, 167449, 87803, 19577, 3001, 599, 157, 43, 15, 52711, 2269733, 1128889, 219613, 27457, 4397, 919, 191, 47
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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A number is prime if and only if it does not lie in Column 1. As a sequence, a permutation of the natural numbers. The fractal sequence of this dispersion is A022447, and the transposition sequence is A114538.
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LINKS
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Clark Kimberling, Interspersions and Dispersions.
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EXAMPLE
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Northwest corner of the array:
1 2 3 5 11 31 127 709 5381 52711 648391...
4 7 17 59 277 1787 15299 167449 2269733 37139213 718064159...
6 13 41 179 1063 8527 87803 1128889 17624813 326851121 7069067389...
8 19 67 331 2221 19577 219613 3042161 50728129 997525853 22742734291...
9 23 83 431 3001 27457 319211 4535189 77557187 1559861749 36294260117...
10 29 109 599 4397 42043 506683 7474967 131807699 2824711961 64988430769...
12 37 157 919 7193 72727 919913 14161729 259336153 5545806481 136395369829...
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MATHEMATICA
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NonPrime[n_] := FixedPoint[n + PrimePi@# + 1 &, n]; t[n_, k_] := Nest[Prime, NonPrime[n], k]; Table[ t[n - k, k], {n, 0, 9}, {k, n, 0, -1}] // Flatten
(* or to view the table *) Table[t[n, k], {n, 0, 6}, {k, 0, 10}] // TableForm (from Robert G. Wilson v (rgwv(at)rgwv.com), Dec 26 2005)
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CROSSREFS
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Columns 1-11: A018252, A007821, A049078, A049079, A049080, A049081, A058322, A058324, A058325, A058326, A058327, A058328, A093046.
Rows 1-7: A007097, A057450, A057451, A057452, A057453, A057456, A057457.
Cf. A007821, A114538, A006450.
Sequence in context: A127008 A064274 A035513 this_sequence A021808 A105081 A026167
Adjacent sequences: A114534 A114535 A114536 this_sequence A114538 A114539 A114540
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Dec 07 2005
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