A226085 Irregular triangular array T(n,k) of consecutive composites.

4, 8, 9, 10, 32, 33, 34, 35, 36, 212, 213, 214, 215, 216, 217, 218, 219, 220, 2312, 2313, 2314, 2315, 2316, 2317, 2318, 2319, 2320, 2321, 2322, 30032, 30033, 30034, 30035, 30036, 30037, 30038, 30039, 30040, 30041, 30042, 30043, 30044, 30045, 30046

Offset

1,1

Comments

Row n contains the p(n+1)-2 consecutive integers between p(1)*p(2)***p(n)+2 and p(1)*p(2)***p(n) + p(n+1)-1 inclusive, where p(n) is the n-th prime.

References

R. L. Graham, D. E. Knuth and O. Patashnick, "Concrete mathematics", Addison Wesley, page 111.

Links

Alois P. Heinz, Rows n = 1..70, flattened

Example

4;
8,    9,    10;
32,   33,   34,   35,   36;
212,  213,  214,  215,  216,  217,  218,  219,  220;
2312, 2313, 2314, 2315, 2316, 2317, 2318, 2319, 2320, 2321, 2322;

Maple

p:= proc(n) p(n):= ithprime(n)*`if`(n=1, 1, p(n-1)) end:
T:= n-> seq(i, i=p(n)+2..p(n)+ithprime(n+1)-1):
seq(T(n), n=1..7);  # Alois P. Heinz, May 25 2013

Mathematica

Table[Range[Product[Prime[n], {n, 1, m}] + 2,
   Product[Prime[n], {n, 1, m}] + Prime[m + 1] - 1], {m, 1,
   6}] // Grid

Crossrefs

Sequence in context: A094349 A118715 A175839 * A104623 A228653 A158758

Adjacent sequences: A226082 A226083 A226084 * A226086 A226087 A226088

Keyword

nonn,tabf

Author

Geoffrey Critzer, May 25 2013

Status

approved