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A185510 Array of primes in the natural number array A000027, by antidiagonals. 2
2, 7, 3, 11, 5, 13, 29, 17, 31, 19, 37, 23, 139, 59, 41, 67, 47, 193, 109, 71, 61, 79, 107, 409, 157, 83, 97, 43, 137, 173, 499, 257, 281, 331, 73, 53, 191, 233, 823, 439, 383, 601, 127, 113, 199, 211, 353, 1381, 599, 1181, 709, 197, 179, 829, 101, 277, 467, 1543, 907, 1601, 1087, 283, 239, 1549, 163, 89 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Start with the natural number array A000027:

1....2.....4....7...11...16...22...29...

3....5.....8...12...17...23...30...38...

6....9....13...18...24...31...39...48...

10...14...19...25...32...40...49...59...

15...20...26...33...41...50...60...71...

21...27...34...42...51...61...72...84...

28...35...43...52...62...73...85...98...

Row n of A185510 shows the primes in row n of A000027:

2....7....11...29...37....67....79...137...(A055469)

3....5....17...23...47...107...173...233...(A055472)

13..31...139..193..409...499...823..1381...(A159047)

19..59...109..157..257...439...599...907...(A159048)

41..71....83..281..383..1181..1601..2351...(A159049)

61..97...331..601..709..1087..1231..2707...

43..73...127..197..283..307...503...673...

Conjecture:  Every row contains infinitely many primes.

LINKS

Table of n, a(n) for n=1..66.

MATHEMATICA

f[n_, k_]:=n+(k+n-2)(k+n-1)/2;

TableForm[Map[Select[#, PrimeQ]&, Table[f[n, k], {n, 1, 20}, {k, 1, 100}]]]

CROSSREFS

Cf. A000027, A000040, A185511.

Sequence in context: A242304 A227415 A051430 * A091578 A258249 A256448

Adjacent sequences:  A185507 A185508 A185509 * A185511 A185512 A185513

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 29 2011

STATUS

approved

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Last modified June 28 09:49 EDT 2017. Contains 288813 sequences.