

A082228


In the following square array numbers (not occurring earlier) are entered like this a(1, 1), a(1, 2), a(2, 1), a(3, 1), a(2, 2), a(1, 3), a(1, 4), a(2, 3), a(3, 2), a(4, 1), a(5, 1), a(4, 2), ... such that every partial sum (n>1) of the rows is composite and every partial sum (n>1) of the columns is prime. Sequence contains the terms in the order in which they are entered.


4



1, 3, 2, 4, 8, 5, 6, 12, 18, 10, 14, 24, 20, 11, 7, 13, 16, 26, 22, 30, 28, 38, 44, 42, 36, 48, 46, 9, 19, 34, 50, 32, 52, 56, 40, 54, 60, 62, 66, 68, 64, 58, 70, 78, 15, 17, 82, 76, 80, 72, 74, 84, 88, 102, 96, 90, 100, 86, 106, 108, 92, 114, 98, 94, 110, 21, 25, 116, 112, 120
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..70.


EXAMPLE

Square array begins
1 3 5 6 ...
2 8 12 ...
4 18 ...
10 24 ...
14 ...
...
E.g., the third partial sum of the second row is 2+8+12 = 22, which is composite, while the same for the second column is 3+8+18 = 29, which is prime.


PROG

(PARI) { A=matrix(100, 100); S=Set(); for(s=2, 101, for(i=1, s1, if(s%2, q=[i, si], q=[si, i]); p=[sum(j=1, q[2]1, A[q[1], j]), sum(j=1, q[1]1, A[j, q[2]])]; n=1; while(setsearch(S, n)  (p[1]&&isprime(p[1]+n))  (p[2]&&!isprime(p[2]+n)), n++); A[q[1], q[2]]=n; S=setunion(S, Set([n])); print1(n, ", "); )) } \\ Max Alekseyev, Apr 11 2009


CROSSREFS

Cf. A082224, A082225, A082226, A082227, A082229, A082230, A082231.
Sequence in context: A201422 A231330 A254051 * A114650 A170949 A276953
Adjacent sequences: A082225 A082226 A082227 * A082229 A082230 A082231


KEYWORD

hard,nonn,tabl


AUTHOR

Amarnath Murthy, Apr 09 2003


EXTENSIONS

Extended by Max Alekseyev, Apr 11 2009


STATUS

approved



