

A124886


3almost prime triangle, read by rows.


2



1, 1, 7, 1, 11, 9, 1, 17, 3, 5, 1, 19, 8, 4, 14, 1, 26, 2, 6, 12, 15, 1, 27, 18, 10, 20, 30, 22, 1, 29, 13, 31, 21, 23, 40, 28, 1, 41, 25, 38, 32, 34, 16, 36, 39, 1, 43, 33, 35, 57, 42, 24, 44, 48, 50
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OFFSET

1,3


COMMENTS

This is to 3almost primes (A014612) as A124883 is to semiprimes (A001358). The nth row is of length n. Each value is the smallest previously unused natural number such that every pair of adjacent values in the triangle is 3almost prime (A014612). Consider row 2. Starting with T(1,2) = 1, the least integer we can add to 1 and get a 3almost prime is 7, since 1 + 8 = 8 = 2^3 is 3almost prime. Consider row 3. Starting with T(1,3) = 1, the least integer we can add to 1 and get a 3almost prime is 7, but we've already used that. The least unused integer that works is 11, since 1 + 11 = 12 = 2^2 * 3 is 3almost prime. If we cross out ones from the triangle read by rows, what remains is a permutation of the natural number greater than 1. That is, every nonnegative integer appears in the triangle. The second column T(n,2) is monotone increasing.


REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, 2nd ed. New York: SpringerVerlag, p. 106, 1994.
M. J. Kenney, "Student Math Notes." NCTM News Bulletin. Nov. 1986.


LINKS

Table of n, a(n) for n=1..55.
Eric Weisstein's World of Mathematics, Prime Triangle.


FORMULA

T(n,1) = 1 for all natural numbers n. For n>1 and 1<k<n we have T(n,k) = min{j such that j<>T(n,i) for i<k and j<>T(r,s) for r<n and for all i<j we have T(i,j) + T(i,j1) is in A014612).


EXAMPLE

Triangle begins:
1.
1..7.
1.11..9.
1.17..3..5.
1.19..8..4.14.
1.26..2..6.12.15.
1.27.18.10.20.30.22.
1.29.13.31.21.23.40.28.
1.41.25.38.32.34.16.36.39.
1.43.33.35.57.42.24.44.48.50.


CROSSREFS

Cf. A001358, A014612, A036440, A051237, A124883.
Sequence in context: A124970 A251768 A178034 * A061195 A232111 A074283
Adjacent sequences: A124883 A124884 A124885 * A124887 A124888 A124889


KEYWORD

easy,nonn,tabl


AUTHOR

Jonathan Vos Post, Nov 12 2006


STATUS

approved



