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

1,2

Comments

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

Links

Table of n, a(n) for n=1..78.

Example

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

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}]]

Crossrefs

Cf. A000027, A000040, A185510.

Sequence in context: A243855 A267185 A065187 * A199855 A127914 A218035

Adjacent sequences: A185508 A185509 A185510 * A185512 A185513 A185514

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 29 2011

Status

approved