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A305579 Square array read by antidiagonals upwards in which row k has k as its first term and each subsequent term is the least possible value such that the sum of any 2 or more terms does not equal a prime. 0
1, 2, 3, 3, 4, 5, 4, 5, 6, 87, 5, 5, 7, 8, 87, 6, 7, 11, 83, 10, 1151, 7, 8, 9, 29, 235, 12, 5371, 8, 8, 10, 79, 215, 395, 14, 199276, 9, 10, 13, 12, 131, 511, 5275, 16, 32281747, 10, 11, 12, 37, 14, 196, 8729, 76128, 18, 16946784207, 11, 11, 13, 14, 67, 16, 3983, 20526, 9782734, 20 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Rows which appear to have consecutive even numbers are for k = 2, 6, 8, 14, 18, 20, 26, 36, 44, 48, 50, 54,56, 68, 74, 78, 86, 96, 114, ..., .
Conjecture: these row terms are a proper subset of A005843.
LINKS
EXAMPLE
Row 1 is A133660 and is a good illustration of the definition.
Array begins:
============================================================================
k\n| 1 2 3 4 5 6 7 8 9 10
---|------------------------------------------------------------------------
1 | 1, 3, 5, 87, 113, 1151, 5371, 199276, 32281747, 16946784207, ..., ;
2 | 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ..., ;
3 | 3, 5, 7, 83, 235, 395, 5275, 76128, 9782734, ..., ;
4 | 4, 5, 11, 29, 215, 511, 8729, 20526, 9745499, ..., ;
5 | 5, 7, 9, 79, 131, 196, 3983, 16380, 270270, ..., ;
6 | 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, ..., ;
7 | 7, 8, 13, 37, 67, 1087, 5128, 137886, 6353767, ..., ;
8 | 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, ..., ;
9 | 9, 11, 13, 71, 112, 281, 1952, 147630, 1729159, ..., ;
10 | 10, 11, 14, 25, 94, 756, 2394, 28480, 1466566, ..., ;
11 | 11, 13, 14, 25, 109, 559, 2719, 57985, 2589731, ..., ;
12 | 12, 13, 14, 37, 79, 673, 2929, 113256, 9708060, ..., ;
13 | 13, 14, 19, 31, 97, 882, 2028, 161340, 3635970, ..., ;
14 | 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, ..., ;
15 | 15, 17, 18, 31, 137, 502, 7983, 599346, 27105801, ..., ;
16 | 16, 17, 18, 47, 107, 395, 6480, 91140, 467730, ..., ;
17 | 17, 18, 21, 31, 77, 637, 3609, 77910, 652680, ..., ;
18 | 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, ..., ;
19 | 19, 20, 25, 30, 61, 235, 2965, 4415, 394170, 5769540, ..., ;
20 | 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, ..., ;
21 | 21, 23, 25, 47, 73, 797, 20419, 235665, ..., ;
22 | 22, 23, 27, 42, 69, 462, 672, 783, 71652, 935298, ..., ;
23 | 23, 25, 26, 37, 73, 1555, 4219, 196260, 3698520, ..., ;
24 | 24, 25, 26, 31, 193, 504, 3756, 91831, 7703843, ..., ;
25 | 25, 26, 29, 31, 39, 750, 4350, 85830, 661350, ..., ;
26 | 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, ..., ;
27 | 27, 28, 29, 35, 232, 888, 5670, 134400, 4058376, ..., ;
28 | 28, 29, 34, 53, 59, 1045, 3696, 249240, 9475589, ..., ;
29 | 29, 31, 33, 55, 57, 674, 6581, 126272, 2549747, ..., ;
30 | 30, 32, 33, 52, 60, 63, 90, 120, 150, 180, ..., ;
31 | 31, 32, 33, 54, 90, 714, 9450, 188850, 2598573, ..., ;
32 | 32, 33, 37, 45, 138, 597, 2703, 101055, 2754885, ..., ;
33 | 33, 35, 37, 47, 133, 555, 4155, 332885, 3090195, ..., ;
34 | 34, 35, 41, 43, 77, 594, 2940, 35700, 2323246, ..., ;
35 | 35, 37, 39, 43, 210, 1061, 10125, 372955, 30373014, ..., ;
36 | 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, ..., ;
37 | 37, 38, 39, 47, 48, 631, 8862, 124851, 4972506, ..., ;
..., etc.
MATHEMATICA
(* first do *) Needs["Combinatorica`"] (* then *) lst = {k}; g[k_] := Block[{j = 1, l = 2^Length@lst}, While[j < l && !PrimeQ[Plus @@ NthSubset[j, lst] + k], j++ ]; If[j == l, False, True]]; f[n_] := Block[{k = lst[[-1]] + 1}, While[PrimeQ@k || g[k] == True, k++; k++ ]; AppendTo[lst, k]; k]; Do[ Print@ f@ n, {n, 10}] (* Robert G. Wilson v, Jun 05 2018 *)
CROSSREFS
Cf. A005843, A052349, A133660, A133661, first column: A000027.
Sequence in context: A094727 A341511 A089308 * A321440 A115729 A115728
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved

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Last modified April 16 12:36 EDT 2024. Contains 371711 sequences. (Running on oeis4.)