A075336 -id:A075336 - cp's OEIS frontend

A075333 Pair up the natural numbers as (r, s) (say) so that all natural numbers are obtained only once as r, s, s+r, s-r or r*s: (2, 3), (4, 11), (8, 17), (10, 22), (13, 27), (16, 34), ... Sequence gives first member of each pair.

2, 4, 8, 10, 13, 16, 19, 21, 23, 28, 30, 33, 36, 38, 42, 43, 48, 52, 54, 55, 60, 63, 65, 69, 71, 75, 77, 80, 82, 84, 87, 92, 94, 96, 98, 102, 104, 107, 111, 113, 116, 119, 121, 124, 126, 128, 134, 137, 140, 142, 144, 148, 150, 153, 154, 159, 162, 166, 168, 172, 174

Offset: 1

Amarnath Murthy, Sep 18 2002

nonn

The first pair starts with 2 and not with 1 as in (1,k) k occurs as 1*k (of the form r*s) and k (of the form s) itself, i.e., in two ways.

Joshua Zucker, Feb 24 2008, Table of n, a(n) for n = 1..151

Cf. A075334, A075335, A075336, A075337.

Corrected and extended by Joshua Zucker, Feb 24 2008

A075334 Second members of pairs in A075333.

Original entry on oeis.org

3, 11, 17, 22, 27, 34, 39, 45, 49, 57, 61, 68, 73, 79, 88, 90, 99, 105, 110, 114, 122, 127, 132, 139, 145, 151, 155, 161, 165, 170, 176, 185, 189, 193, 198, 205, 210, 215, 223, 228, 234, 239, 244, 249, 255, 259, 269, 275, 281, 285, 290, 297, 302, 309, 312, 319

Offset: 1

Amarnath Murthy, Sep 18 2002

nonn

Joshua Zucker, Feb 24 2008, Table of n, a(n) for n = 1..151

Cf. A075333, A075335, A075336, A075337.

More terms from Joshua Zucker, Feb 24 2008

A075335 Differences of members of pairs in A075333.

Original entry on oeis.org

1, 7, 9, 12, 14, 18, 20, 24, 26, 29, 31, 35, 37, 41, 46, 47, 51, 53, 56, 59, 62, 64, 67, 70, 74, 76, 78, 81, 83, 86, 89, 93, 95, 97, 100, 103, 106, 108, 112, 115, 118, 120, 123, 125, 129, 131, 135, 138, 141, 143, 146, 149, 152, 156, 158, 160, 163, 167, 171, 173, 175

Offset: 1

Amarnath Murthy, Sep 18 2002

nonn

Joshua Zucker, Feb 24 2008, Table of n, a(n) for n = 1..151

Cf. A075333, A075334, A075336, A075337.

More terms from Joshua Zucker, Feb 24 2008

A075337 Products of members of pairs in A075333.

Original entry on oeis.org

6, 44, 136, 220, 351, 544, 741, 945, 1127, 1596, 1830, 2244, 2628, 3002, 3696, 3870, 4752, 5460, 5940, 6270, 7320, 8001, 8580, 9591, 10295, 11325, 11935, 12880, 13530, 14280, 15312, 17020, 17766, 18528, 19404, 20910, 21840, 23005, 24753, 25764

Offset: 1

Amarnath Murthy, Sep 18 2002

nonn

Joshua Zucker, Feb 24 2008, Table of n, a(n) for n = 1..151

Cf. A075333, A075334, A075335, A075336.

More terms from Joshua Zucker, Feb 24 2008

A249055 a(1)=0; the next term is always the product of the two smallest numbers not yet in the sequence and which have not yet been used.

Original entry on oeis.org

0, 2, 12, 30, 56, 90, 143, 210, 272, 342, 420, 506, 600, 702, 812, 992, 1122, 1260, 1406, 1560, 1722, 1892, 2070, 2256, 2450, 2652, 2862, 3135, 3422, 3660, 3906, 4160, 4422, 4692, 4970, 5256, 5550, 5852, 6162, 6480, 6806, 7140, 7482, 7832, 8372, 8742, 9120, 9506, 9900

Offset: 1

N. J. A. Sloane, Nov 01 2014

nonn

Suggested by A075336 and A249406.

			Start with a(1) = 0. The missing numbers are 1 2 3 4 5 6 ...
Multiply the first two, and we get 2, which is therefore a(2).
Cross 1, 2, and 1*2 = 2 off the missing list.
The first two missing numbers are now 3 and 4, so a(3) = 3*4 = 12.
Cross off 3,4,12 from the missing list.
Repeat!

Cf. A075326, A000045, A249406, A000304, A000301.

M:=50; A:=[0]; miss:=[seq(n,n=1..M^2)]:
for n from 1 to M do t1:=miss[1]*miss[2]; A:=[op(A),t1];
miss:=[seq(miss[i],i=3..nops(miss))];
miss:=remove('x->x=t1',miss);
od:
A;

Typo in definition corrected by Douglas Latimer, Nov 01 2014

cp's OEIS Frontend

A075333 Pair up the natural numbers as (r, s) (say) so that all natural numbers are obtained only once as r, s, s+r, s-r or r*s: (2, 3), (4, 11), (8, 17), (10, 22), (13, 27), (16, 34), ... Sequence gives first member of each pair.

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A075334 Second members of pairs in A075333.

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A075335 Differences of members of pairs in A075333.

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A075337 Products of members of pairs in A075333.

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A249055 a(1)=0; the next term is always the product of the two smallest numbers not yet in the sequence and which have not yet been used.

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