%I A114537
%S A114537 1,2,4,3,7,6,5,17,13,8,11,59,41,19,9,31,277,179,67,23,10,127,1787,1063,
%T A114537 331,83,29,12,709,15299,8527,2221,431,109,37,14,5381,167449,87803,19577,
%U A114537 3001,599,157,43,15,52711,2269733,1128889,219613,27457,4397,919,191,47
%N A114537 Dispersion of the primes (an array read by antidiagonals).
%C A114537 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.
%H A114537 Clark Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/
               intersp.html">Interspersions and Dispersions</a>.
%e A114537 Northwest corner of the array:
%e A114537 1 2 3 5 11 31 127 709 5381 52711 648391...
%e A114537 4 7 17 59 277 1787 15299 167449 2269733 37139213 718064159...
%e A114537 6 13 41 179 1063 8527 87803 1128889 17624813 326851121 7069067389...
%e A114537 8 19 67 331 2221 19577 219613 3042161 50728129 997525853 22742734291...
%e A114537 9 23 83 431 3001 27457 319211 4535189 77557187 1559861749 36294260117...
%e A114537 10 29 109 599 4397 42043 506683 7474967 131807699 2824711961 64988430769...
%e A114537 12 37 157 919 7193 72727 919913 14161729 259336153 5545806481 136395369829...
%t A114537 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
%t A114537 (* 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)
%Y A114537 Columns 1-11: A018252, A007821, A049078, A049079, A049080, A049081, A058322, 
               A058324, A058325, A058326, A058327, A058328, A093046.
%Y A114537 Rows 1-7: A007097, A057450, A057451, A057452, A057453, A057456, A057457.
%Y A114537 Cf. A007821, A114538, A006450.
%Y A114537 Sequence in context: A127008 A064274 A035513 this_sequence A021808 A105081 
               A026167
%Y A114537 Adjacent sequences: A114534 A114535 A114536 this_sequence A114538 A114539 
               A114540
%K A114537 nonn,tabl
%O A114537 1,2
%A A114537 Clark Kimberling (ck6(AT)evansville.edu), Dec 07 2005