A185511 Array: row n shows numbers m such that prime(m) is in row n of the natural number array A000027, by antidiagonals.

1, 4, 2, 5, 3, 6, 10, 7, 11, 8, 12, 9, 34, 17, 13, 19, 15, 44, 29, 20, 18, 22, 28, 80, 37, 23, 25, 14, 33, 40, 95, 55, 60, 67, 21, 16, 43, 51, 143, 85, 76, 110, 31, 30, 46, 47, 71, 221, 109, 194, 127, 45, 41, 145, 26, 59, 91, 243, 155, 252, 181, 61, 52, 244, 38, 24, 75, 103, 314, 175, 349, 202, 63, 72, 316, 42, 32, 27

Offset: 1

Author

Clark Kimberling, Jan 29 2011

Keywords

• nonn
• tabl

Comments

If the conjecture at A185510 is true, then the A185512, as a sequence, is a permutation of the natural numbers.

Examples

			Start with the natural number array A000027:
1...2...4...7
3...5...8..12
6...9..13..18
(The antidiagonals are 1; 2,3; 4,5,6; 7,8,9,10;...).
Primes, by rows (A185510):
2.....7....11....29... in row 1 of A000027
3.....5....17....23... in row 2
13...31...139...193... in row 3, etc.
Now replace each prime by its index to obtain A185511.
Northwest corner:
1.....4....5...10...12...19...22...33
2.....3....7....9...15...28...40...51
6....11...34...44...80...95..143..221
8....17...29...37...55...85..109..155
13...20...23...60...76..194..252..349
		

Crossrefs

Cf. A000027, A000040, A185510.

Programs

Mathematica

f[n_,k_]:=n+(k+n-2) (k+n-1)/2;
Do[t[n]={};Do[If[PrimeQ[f[n,k]],AppendTo[t[n],f[n,k]]],{k,1,1000}]; t[n];
u[n]={};Do[If[MemberQ[t[n],Prime[m]],AppendTo[u[n],m]],{m,1,1000}],{n,12}]
TableForm[Table[u[n],{n,12}]]