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 1-8 of 8 results.

A098376 Right edge T(n,0) of the triangle A097883.

Original entry on oeis.org

1, 2, 5, 6, 13, 14, 27, 26, 43, 36, 65, 62, 87, 80, 117, 110, 147, 146, 185, 168, 221, 210, 271, 258, 323, 308, 369, 368, 427, 414, 491, 476, 555, 544, 621, 610, 687, 682, 765, 764, 853, 828, 937, 918, 1027, 1010, 1113, 1102, 1209, 1198, 1305, 1304, 1415, 1398
Offset: 0

Views

Author

Leroy Quet and Robert G. Wilson v, Sep 04 2004

Keywords

Crossrefs

Cf. A097883, A098377.

Programs

  • Mathematica
    a[0, 0] = 1; a[m_, n_] := a[m, n] = Block[{p = Sort[ Flatten[ Join[ Table[ a[i, j], {i, 0, m - 1}, {j, 0, i}], Table[ a[i, j], {i, m, m}, {j, 0, n - 1}]] ]]}, k = Complement[ Range[ p[[ -1]] + 1], p][[1]]; While[ Position[p, k] != {} || If[n == 0, GCD[k, a[m - 1, 0]] != 1, If[n == m, GCD[k, a[m - 1, m - 1]] != 1, GCD[k, a[m - 1, n]] != 1 || GCD[k, a[m - 1, n - 1]] != 1]], k++ ]; k]; Table[ a[m, 0], {m, 0, 53}]

Formula

a(n) = A097883(t+1) where t is a triangular number.

A098377 Left edge T(n,n) or the main diagonal of the triangle A097883.

Original entry on oeis.org

1, 3, 4, 11, 12, 25, 22, 39, 40, 57, 58, 89, 78, 115, 112, 141, 142, 183, 182, 225, 226, 269, 252, 319, 312, 365, 364, 423, 422, 487, 474, 559, 534, 629, 600, 701, 680, 759, 758, 849, 842, 935, 912, 1025, 1008, 1117, 1100, 1203, 1190, 1311, 1300, 1419, 1400
Offset: 0

Views

Author

Leroy Quet and Robert G. Wilson v, Sep 04 2004

Keywords

Crossrefs

Cf. A097883, A098376.

Programs

  • Mathematica
    a[0, 0] = 1; a[m_, n_] := a[m, n] = Block[{p = Sort[ Flatten[ Join[ Table[ a[i, j], {i, 0, m - 1}, {j, 0, i}], Table[ a[i, j], {i, m, m}, {j, 0, n - 1}]] ]]}, k = Complement[ Range[ p[[ -1]] + 1], p][[1]]; While[ Position[p, k] != {} || If[n == 0, GCD[k, a[m - 1, 0]] != 1, If[n == m, GCD[k, a[m - 1, m - 1]] != 1, GCD[k, a[m - 1, n]] != 1 || GCD[k, a[m - 1, n - 1]] != 1]], k++ ]; k]; Table[ a[m, m], {m, 0, 52}]

Formula

a(n) = A097883(t) where t is a triangular number.

A098379 Maximum entry in the n-th row of the triangle A097883.

Original entry on oeis.org

1, 3, 7, 11, 19, 25, 37, 41, 53, 61, 77, 89, 101, 121, 131, 149, 167, 183, 205, 225, 247, 269, 293, 319, 349, 373, 401, 425, 457, 487, 527, 559, 583, 629, 655, 701, 731, 779, 807, 851, 887, 935, 971, 1025, 1061, 1117, 1155, 1213, 1253, 1315, 1357, 1419, 1461
Offset: 0

Views

Author

Leroy Quet and Robert G. Wilson v, Sep 04 2004

Keywords

Comments

All entries are odd.

Crossrefs

Cf. A097883, A098380.

Programs

  • Mathematica
    a[0, 0] = 1; a[m_, n_] := a[m, n] = Block[{p = Sort[ Flatten[ Join[ Table[ a[i, j], {i, 0, m - 1}, {j, 0, i}], Table[ a[i, j], {i, m, m}, {j, 0, n - 1}]] ]]}, k = Complement[ Range[ p[[ -1]] + 1], p][[1]]; While[ Position[p, k] != {} || If[n == 0, GCD[k, a[m - 1, 0]] != 1, If[n == m, GCD[k, a[m - 1, m - 1]] != 1, GCD[k, a[m - 1, n]] != 1 || GCD[k, a[m - 1, n - 1]] != 1]], k++ ]; k]; Table[ Max[ Table[ a[m, n], {n, 0, m}]], {m, 0, 52}]

A098380 Minimum entry in the n-th row of the triangle A097883.

Original entry on oeis.org

1, 2, 4, 6, 10, 14, 18, 24, 32, 36, 42, 60, 66, 80, 96, 110, 126, 144, 160, 168, 196, 210, 238, 258, 284, 308, 334, 360, 388, 414, 442, 476, 502, 540, 568, 610, 638, 682, 710, 756, 786, 828, 870, 918, 952, 1010, 1038, 1102, 1140, 1198, 1236, 1290, 1332, 1398
Offset: 0

Views

Author

Leroy Quet and Robert G. Wilson v, Sep 04 2004

Keywords

Comments

All entries are even except for 1.

Crossrefs

Cf. A097883, A098379.

Programs

  • Mathematica
    a[0, 0] = 1; a[m_, n_] := a[m, n] = Block[{p = Sort[ Flatten[ Join[ Table[ a[i, j], {i, 0, m - 1}, {j, 0, i}], Table[ a[i, j], {i, m, m}, {j, 0, n - 1}]] ]]}, k = Complement[ Range[ p[[ -1]] + 1], p][[1]]; While[ Position[p, k] != {} || If[n == 0, GCD[k, a[m - 1, 0]] != 1, If[n == m, GCD[k, a[m - 1, m - 1]] != 1, GCD[k, a[m - 1, n]] != 1 || GCD[k, a[m - 1, n - 1]] != 1]], k++ ]; k]; Table[ Min[ Table[ a[m, n], {n, 0, m}]], {m, 0, 50}]

A098381 Difference between the number of odd entries and the number of even entries of the n-th row of the triangle A097883.

Original entry on oeis.org

1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 4, -3, 4, -3, 4, -3, 4, -3, 6, -3, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 8, -7, 10, -9
Offset: 1

Views

Author

Leroy Quet and Robert G. Wilson v, Sep 04 2004

Keywords

Comments

a(n+1)-a(n) is odd and alternates in sign (after the eleventh term), at least up through the 125th row.
|a(j+1)-a(j)| >= |a(i+1)-a(i)| for all j>=i and the absolute difference results in 11 ones, 9 threes, 1 five, 7 sevens, 2 nines, 1 eleven, 0 thirteens, 69 fifteens, 1 seventeen, etc.

Examples

			a(6)=2 because the sixth row of the triangle A097883 has entries {14, 15, 16, 21, 23, 25}: 4 odd entries less 2 even entries.

Crossrefs

Cf. A097883, A098382.

Programs

  • Mathematica
    a[0, 0] = 1; a[m_, n_] := a[m, n] = Block[{p = Sort[ Flatten[ Join[ Table[ a[i, j], {i, 0, m - 1}, {j, 0, i}], Table[ a[i, j], {i, m, m}, {j, 0, n - 1}]] ]]}, k = Complement[ Range[ p[[ -1]] + 1], p][[1]]; While[ Position[p, k] != {} || If[n == 0, GCD[k, a[m - 1, 0]] != 1, If[n == m, GCD[k, a[m - 1, m - 1]] != 1, GCD[k, a[m - 1, n]] != 1 || GCD[k, a[m - 1, n - 1]] != 1]], k++ ]; k]; Table[Plus @@ (2Mod[Table[ a[m, n], {n, 0, m}], 2] - 1), {m, 0, 105}]

A098404 Row sums of the triangle A097883.

Original entry on oeis.org

1, 5, 16, 34, 71, 114, 184, 256, 381, 507, 678, 889, 1094, 1406, 1673, 2075, 2460, 2940, 3453, 4015, 4658, 5357, 6066, 6974, 7807, 8845, 9814, 11038, 12193, 13596, 14920, 16522, 17815, 19869, 21282, 23556, 25159, 27671, 29480, 32236, 34301, 37275
Offset: 1

Views

Author

Leroy Quet and Robert G. Wilson v, Sep 06 2004

Keywords

Crossrefs

Cf. A097883.

Programs

  • Mathematica
    a[0, 0] = 1; a[m_, n_] := a[m, n] = Block[{p = Sort[ Flatten[ Join[ Table[ a[i, j], {i, 0, m - 1}, {j, 0, i}], Table[ a[i, j], {i, m, m}, {j, 0, n - 1}]] ]]}, k = Complement[ Range[ p[[ -1]] + 1], p][[1]]; While[ Position[p, k] != {} || If[n == 0, GCD[k, a[m - 1, 0]] != 1, If[n == m, GCD[k, a[m - 1, m - 1]] != 1, GCD[k, a[m - 1, n]] != 1 || GCD[k, a[m - 1, n - 1]] != 1]], k++ ]; k]; Table[ Sum[ a[m, n], {n, 0, m}], {m, 0, 41}]

A098382 Partial sums of A098381.

Original entry on oeis.org

1, 1, 2, 2, 3, 5, 6, 6, 7, 7, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14, 13, 17, 14, 18, 15, 19, 16, 20, 17, 23, 20, 28, 21, 29, 22, 30, 23, 31, 24, 32, 25, 33, 26, 34, 27, 35, 28, 36, 29, 37, 30, 38, 31, 39, 32, 40, 33, 41, 34, 42, 35, 43, 36, 44, 37, 45, 38, 46, 39, 47, 40, 48, 41
Offset: 1

Views

Author

Leroy Quet and Robert G. Wilson v, Sep 04 2004

Keywords

Comments

a(2n+2)>a(2n) and a(2n+1)>a(2n-1), at least up through the 125th row.

Crossrefs

Cf. A097883, A098381.

Programs

  • Mathematica
    a[ 0, 0 ] = 1; a[ m_, n_ ] := a[ m, n ] = Block[ {p = Sort[ Flatten[ Join[ Table[ a[ i, j ], {i, 0, m - 1}, {j, 0, i} ], Table[ a[ i, j ], {i, m, m}, {j, 0, n - 1} ] ] ] ]}, k = Complement[ Range[ p[ [ -1 ] ] + 1 ], p ][ [ 1 ] ]; While[ Position[ p, k ] != {} || If[ n == 0, GCD[ k, a[ m - 1, 0 ] ] != 1, If[ n == m, GCD[ k, a[ m - 1, m - 1 ] ] != 1, GCD[ k, a[ m - 1, n ] ] != 1 || GCD[ k, a[ m - 1, n - 1 ] ] != 1 ] ], k++ ]; k ]; t = Table[ Plus @@ (2Mod[ Table[ a[ m, n ], {n, 0, m} ], 2 ] - 1), {m, 0, 75} ]; Table[ Plus @@ Take[ t, n ], {n, 73} ]

A359752 Lexicographically earliest array of distinct positive integers read by antidiagonals such that integers in cells which are a knight's move apart are coprime.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 6, 8, 9, 11, 13, 17, 19, 23, 10, 12, 15, 21, 27, 16, 14, 22, 25, 29, 31, 37, 20, 33, 18, 24, 35, 26, 39, 41, 43, 47, 49, 53, 59, 61, 32, 55, 67, 45, 28, 30, 51, 57, 63, 34, 36, 71, 73, 38, 44, 40, 65, 79, 83, 89, 85, 77, 91, 69, 42, 75
Offset: 1

Views

Author

Jodi Spitz, Mar 07 2023

Keywords

Examples

			The array begins:
   1  2  4  6 13 12 22 18 ...
   3  5  8 17 15 25 24 ...
   7  9 19 21 29 35 ...
  11 23 27 31 26 ...
  10 16 37 39 ...
  14 20 41 ...
  33 43 ...
  47 ...

Links

Crossrefs

Cf. A097883.

Programs

  • PARI
    See Links section.

Extensions

More terms from Rémy Sigrist, Mar 09 2023
More terms from Jodi Spitz, Mar 10 2023
Showing 1-8 of 8 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.