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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
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 (list; table; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A135853 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

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Last modified January 24 07:13 EST 2020. Contains 331189 sequences. (Running on oeis4.)