A082228 In the following square array A(n,k), 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 (of length > 1) of the rows is composite and every partial sum (of length > 1) of the columns is prime. The sequence contains the terms in the order in which they are entered (with A(1,1) = 1).

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

Offset

1,2

Links

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

Example

Square array A(n,k) (with rows n >= 1 and columns k >= 1) begins
   1,  3,  5,  6,  7, 13, 9, ...
   2,  8, 12, 11, 16, 46, ...
   4, 18, 20, 26, 48, ...
  10, 24, 22, 36, ...
  14, 30, 42, ...
  28, 44,
  38, ...
  ...
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.
From Petros Hadjicostas, Feb 25 2021: (Start)
A(1,2) = 3 because i = 1, j = 2 > 1, and 1 + 3 = 4, which is composite. (The number 2 has been rejected because 1 + 2 = 3, which is prime.)
A(2,1) = 2 because i = 2 > 1, j = 1, and 1 + 2 = 3, which is prime.
A(3,1) = 4 because i = 3 > 1, j = 1, and 1 + 2 + 4 = 7, which is prime.
A(2,2) = 8 because i = j = 2 > 1, 2 + 8 = 10, which is composite, while 3 + 8 = 11, which is prime. (The number 5 has been rejected because 2 + 5 = 7, which is prime; the number 6 has been rejected because 3 + 6 = 9, which is composite; and 7 has been rejected because 3 + 7 = 10, which is composite.)
A(1,3) = 5 because i = 1, j = 3 > 1, and 1 + 3 + 5 = 9, which is composite. (End)

Prog

(PARI) lista(nn) = { my(A=matrix(nn, nn)); S=Set(); for(s=2, nn+1, for(i=1, s-1, if(s%2, q=[i, s-i], q=[s-i, 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 [Slightly edited by Petros Hadjicostas, Feb 25 2021]

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