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A138947 Square array T[i+1,j] = prime(T[i,j]), T[1,j] = j-th nonprime = A018252(j); read by upward antidiagonals. 3


%S 1,4,2,6,7,3,8,13,17,5,9,19,41,59,11,10,23,67,179,277,31,12,29,83,331,

%T 1063,1787,127,14,37,109,431,2221,8527,15299,709,15,43,157,599,3001,

%U 19577,87803

%N Square array T[i+1,j] = prime(T[i,j]), T[1,j] = j-th nonprime = A018252(j); read by upward antidiagonals.

%C For i>1, T[i,j] = A018252(j)-th number among those not occurring in rows < i.

%C A permutation of the integers > 0.

%C Transpose of A114537. See that sequence and the link for more information and references.

%D Alexandrov, Lubomir. "On the nonasymptotic prime number distribution." arXiv preprint math/9811096 (1998). (See Appendix.)

%H N. Fernandez, <a href="http://www.borve.org/primeness/FOP.html">An order of primeness, F(p)</a>.

%H N. Fernandez, <a href="/A006450/a006450.html">An order of primeness</a> [cached copy, included with permission of the author]

%F T[i,j] = j-th number for which A078442 equals i-1.

%e The first row (1,4,6,8,9,10...) of the array gives the nonprime numbers A018252.

%e The 2nd row (2,7,13,19,23,29,37,...) of the array gives the primes with nonprime index, A000040(A018252(j)) = A007821(j).

%e The i-th row is { A000040(k) | A049076(k)=i-1 } = A078442^{-1}(i-1).

%e Column j is the sequence b(n+1)=prime(b(n)) starting with b(j)=A018252(j): A007097, A057450, A057451, A057452, A057453, A057456, A057457, ...

%t t[1, 1] = 1; t[1, 2] = 4; t[1, k_] := (p = t[1, k-1]; If[ PrimeQ[p+1], p+2, p+1]); t[n_ /; n > 1, k_] := Prime[t[n-1, k]]; Flatten[ Table[ t[n, k-n+1], {k, 1, 9}, {n, 1, k}]] (* _Jean-Fran├žois Alcover_, Oct 03 2011 *)

%o (PARI) p=c=0; T=matrix( 10,10, i,j, if( i==1, while( isprime(c++),); p=c, p=prime(p))); A138947=concat( vector( vecmin( matsize( T )),i, vector( i,j, T[ j,i+1-j ])))

%Y Cf. A018252, A007821, A006450, A049076, A007097.

%Y If the antidiagonals are read in the opposite direction we get A114537.

%K nonn,tabl

%O 1,2

%A _M. F. Hasler_, Apr 28 2008

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Last modified September 29 14:13 EDT 2020. Contains 337431 sequences. (Running on oeis4.)