cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A133660 No sum of 2 or more terms equals a prime.

Original entry on oeis.org

1, 3, 5, 87, 113, 1151, 5371, 199276, 32281747, 16946784207
Offset: 1

Views

Author

Randy L. Ekl, Dec 28 2007

Keywords

Comments

Sequence is infinite since the primes have density 0. - Charles R Greathouse IV, Apr 28 2011

Examples

			5 is a term of the series, as 5+1, 5+3 and 5+3+1 are all nonprime. The next term, 87, is the next number k such that k+1, k+3, k+1+3, k+5, k+1+5, k+3+5 and k+1+3+5 are all nonprime.

Crossrefs

Cf. A052349, A133661.

Programs

  • Mathematica
    (* first do *) Needs["Combinatorica`"] (* then *) lst = {}; 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[g[k] == True, k++ ]; AppendTo[lst, k]; k]; Do[Print@f@n, {n, 10}]; (* Robert G. Wilson v, Dec 31 2007 *)
(* Second program, avoids "Combinatorica`": *)
Nest[Append[#, Block[{k = Last@ # + 1}, While[AnyTrue[Total /@ Select[Subsets[Append[#, k]], Length@ # > 1 &], PrimeQ],k++ ]; k ] ] &, {1}, 6] (* Michael De Vlieger, Jun 11 2018 *)

Extensions

a(9) from Robert G. Wilson v, Dec 31 2007
a(10) from Donovan Johnson, Feb 15 2008

A133266 a(1) = 30; for n >= 2, choose smallest a(n) so that no sum of 2 or more terms equals a prime.

Original entry on oeis.org

30, 32, 33, 52, 60, 63, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, 450, 480, 510, 540, 570, 600, 630, 660, 690, 720, 750, 780
Offset: 1

Views

Author

Robert G. Wilson v, Jan 01 2008

Keywords

Crossrefs

Cf. A052349, A133660, A133661.

Programs

  • Mathematica
    (* first do *) Needs [ "Combinatorica`" ] (* then *) lst = {30}; 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 [ g@k == True, k++ ]; AppendTo [ lst, k ]; k ]; Do [ Print@ f@n, {n, 30} ]

Formula

a(n+1) = a(n) + 30 for n >= 7 (conjectured). - Chai Wah Wu, Feb 15 2020

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.

Original entry on oeis.org

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
Offset: 1

Views

Author

Randy L. Ekl and Robert G. Wilson v, Jun 05 2018

Keywords

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.

Examples

			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.

Crossrefs

Cf. A005843, A052349, A133660, A133661, first column: A000027.

Programs

  • 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 *)
Showing 1-3 of 3 results.

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