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

1,2

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.

References

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

Links

Table of n, a(n) for n=1..43.

N. Fernandez, An order of primeness, F(p).

N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Formula

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

Example

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, ...

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 *)

Prog

(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 ])))

Crossrefs

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

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

Sequence in context: A338915 A173197 A256568 * A083412 A086399 A105365

Adjacent sequences: A138944 A138945 A138946 * A138948 A138949 A138950

Keyword

nonn,tabl

Author

M. F. Hasler, Apr 28 2008

Status

approved