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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.
Every prime occurs exactly once; that is, every prime is uniquely expressible as (1/2)(n^2 + (2k-1)n + (k-2)(k-1)) for some positive integers n and k. We assume as true the conjecture that each row is infinite. - Clark Kimberling, Mar 10 2020
LINKS
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
Sequence in context: A309156 A298042 A051430 * A304754 A091578 A332363
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jan 29 2011
STATUS
approved

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Last modified April 20 06:42 EDT 2024. Contains 371799 sequences. (Running on oeis4.)