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 1-6 of 6 results.

A153136 Smallest sequence of primes such that no sum of at least two terms is prime.

Original entry on oeis.org

2, 7, 13, 43, 103, 1627, 25349, 315743, 7338823, 42939980423
Offset: 1

Views

Author

Benoit Jubin, Dec 19 2008

Keywords

Crossrefs

Cf. A153137, A153138, A133660, A052349, A254337, A254341.

Programs

  • PARI
    a=[];for(n=1,10, forprime(p=2,,setsearch(a,p)&&next;for(i=1,2^#a-1,isprime(normlp(vecextract(a,i),1)+p)&&next(2));a=concat(a,p);print1(p","))) \\ Very simplistic, should at least avoid an odd number of odd primes in the partial sum of earlier terms. \\ M. F. Hasler, Jan 29 2015

Extensions

a(8)-a(10) from Donovan Johnson, Dec 23 2008

A133661 No sum of 2 or more terms equals a prime, terms alternate parity and there are no primes in the list.

Original entry on oeis.org

1, 8, 25, 86, 209, 472, 25719, 238350, 41931245, 14426603100
Offset: 1

Views

Author

Randy L. Ekl, Dec 28 2007

Keywords

Comments

a(10) > 263811880. - Robert G. Wilson v, Jan 01 2008

Examples

			25 is a term, because 25 is odd (previous term was even), 25 is composite and 25+1, 25+8 and 25+8+1 are all composite.

Crossrefs

Cf. A052349, A133660.

Programs

  • Mathematica
    (* first do *) Needs["Combinatorica`"] (* then *) lst = {1, 8}; 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, Jan 01 2008 *)

Extensions

a(9) from Robert G. Wilson v, Jan 01 2008
a(10) from Donovan Johnson, Feb 15 2008

A153137 Smallest sequence of noncomposite numbers such that no sum of at least two terms is prime.

Original entry on oeis.org

1, 3, 5, 113, 181, 661, 10891, 927149, 88070399, 15288362671
Offset: 1

Views

Author

Benoit Jubin, Dec 19 2008

Keywords

Crossrefs

Cf. A153136, A153138, A133660, A052349, A254337, A254341.

Programs

  • PARI
    print1(1); a=[1]; for(n=1, 10, forprime(p=vecmin(a)+1, , setsearch(a, p)&&next; for(i=1, 2^#a-1, isprime(normlp(vecextract(a, i), 1)+p)&&next(2)); a=concat(a, p); print1(","p))) \\ Very simplistic, should at least avoid an odd number of terms in the partial sum of earlier terms. \\ M. F. Hasler, Jan 29 2015

Extensions

a(8)-a(10) from Donovan Johnson, Dec 23 2008

A153138 Smallest sequence of odd primes such that no sum of at least two terms is prime.

Original entry on oeis.org

3, 5, 7, 83, 317, 383, 29567, 423509, 118661483, 52542428123
Offset: 1

Views

Author

Benoit Jubin, Dec 19 2008

Keywords

Crossrefs

Cf. A153136, A153137, A133660, A052349, A254337, A254341.

Programs

  • PARI
    a=[]; for(n=1, 10, forprime(p=if(a,a[#a]+2,3), , setsearch(a, p)&&next; for(i=1, 2^#a-1, isprime(normlp(vecextract(a, i), 1)+p)&&next(2)); a=concat(a, p); print1(p", "))) \\ Very simplistic, should at least avoid an odd number of terms in the partial sum of earlier terms. \\ M. F. Hasler, Jan 29 2015

Extensions

a(8)-a(10) from Donovan Johnson, Dec 23 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 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.