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

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, 1063, 1787, 127, 14, 37, 109, 431, 2221, 8527, 15299, 709, 15, 43, 157, 599, 3001, 19577, 87803

Offset: 1

Author

M. F. Hasler, Apr 28 2008

Keywords

• nonn
• tabl

Comments

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

A permutation of the integers > 0.

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

Examples

			The first row (1,4,6,8,9,10...) of the array gives the nonprime numbers A018252.
The 2nd row (2,7,13,19,23,29,37,...) of the array gives the primes with nonprime index, A000040(A018252(j)) = A007821(j).
The i-th row is { A000040(k) | A049076(k)=i-1 } = A078442^{-1}(i-1).
Column j is the sequence b(n+1)=prime(b(n)) starting with b(j)=A018252(j): A007097, A057450, A057451, A057452, A057453, A057456, A057457, ...
		

References

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

Links

• N. Fernandez, An order of primeness, F(p).
• N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Crossrefs

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

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

Programs

Mathematica

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-François Alcover, Oct 03 2011 *)

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 ])))

Formula

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