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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
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
If the antidiagonals are read in the opposite direction we get A114537.
Sequence in context: A338915 A173197 A256568 * A083412 A086399 A105365
KEYWORD
nonn,tabl
AUTHOR
M. F. Hasler, Apr 28 2008
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)