A254204 T(n,k) = number of length n 1..(k+2) arrays with no leading or trailing partial sum equal to a prime.

1, 2, 0, 2, 1, 0, 3, 1, 2, 0, 3, 4, 4, 6, 1, 4, 4, 17, 9, 11, 0, 5, 11, 18, 54, 21, 27, 0, 6, 16, 47, 59, 176, 47, 53, 1, 6, 23, 68, 195, 204, 610, 118, 133, 0, 7, 23, 119, 315, 898, 769, 2197, 333, 310, 0, 7, 34, 131, 676, 1653, 4353, 3098, 8358, 984, 691, 1, 8, 34, 226, 786, 4078

Offset

1,2

Comments

Table starts

.1...2....2......3......3.......4.......5........6........6.........7.........7

.0...1....1......4......4......11......16.......23.......23........34........34

.0...2....4.....17.....18......47......68......119......131.......226.......237

.0...6....9.....54.....59.....195.....315......676......786......1571......1743

.1..11...21....176....204.....898....1653.....4078.....5075.....11512.....13456

.0..27...47....610....769....4353....9126....25389....33798.....85437....105502

.0..53..118...2197...3098...22189...50166...156454...222665....640886....845325

.1.133..333...8358..14080..112015..266060...972441..1504758...4956259...6973431

.0.310..984..34005..63868..542397.1445197..6288889.10555156..38994996..58337721

.0.691.3362.132483.261240.2658643.8388620.41384162.74476895.308256904.493751257

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 antidiagonals; terms 1..264 from R. H. Hardin)

Example

Some solutions for n=4 k=4
..4....6....4....4....6....4....1....4....6....6....1....4....6....6....1....6
..2....4....5....2....6....6....3....6....6....4....5....4....6....6....3....3
..2....4....3....4....3....5....6....6....3....2....6....4....6....2....2....5
..6....4....6....4....1....1....6....4....6....4....4....4....4....4....4....4

Prog

(PARI)
step(v, k, oks)={vector(#v, i, if(oks(i), sum(j=1, min(k, i-1), v[i-j])))}
U(n, k, s, f) = {if(f(s), my(m=vector(s, i, f(i) && f(s-i)), v=vector(#m, i, i<=k&&m[i])); for(i=2, n, v=step(v, k, j->j>=i&&j<=s-n+i&&m[j])); v[s], 0)}
T(n, k) = {sum(s=n, n*(k+2), U(n, k+2, s, i->!isprime(i)))} \\ Andrew Howroyd, Nov 29 2025

Crossrefs

Columns 1..7 are A254197, A254198, A254199, A254200, A254201, A254202, A254203.

Rows 1..7 are A062298(n+2), A254205, A254206, A254207, A254208, A254209, A254210.

Sequence in context: A127371 A036849 A097364 * A321361 A319517 A321460

Adjacent sequences: A254201 A254202 A254203 * A254205 A254206 A254207

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 26 2015

Status

approved