

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
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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+n2) (k+n1)/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



