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A185511 Array:  row n shows numbers m such that prime(m) is in row n of the natural number array A000027, by antidiagonals. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 5 03:59 EST 2021. Contains 349530 sequences. (Running on oeis4.)