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.

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A291495 The arithmetic function u(n,8,7).

Original entry on oeis.org

50, 44, 45, 32, 40, 44, 50, 8, 9, 10, 11, 12, 13, 14, 15, 8, 17, 9, 19, 10, 21, 11, 23, 8, 25, 13, 9, 14, 29, 10, 31, 8, 11, 17, 35, 9, 37, 19, 13, 8, 41, 14, 43, 11, 9, 23, 47, 8, 49, 10, 17, 13, 50, 9, 11, 8, 19, 29, 50, 10, 50, 31, 9, 8, 13, 11, 50, 17, 23, 10
Offset: 1

Views

Author

Robert Price, Aug 24 2017

Keywords

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Programs

  • Mathematica
    u[n_, m_, h_] := (d = Divisors[n]; Min[(h*Ceiling[m/d] - h + 1)*d]); Table[u[n, 8, 7], {n, 1, 70}]

A291496 The arithmetic function u(n,8,8).

Original entry on oeis.org

57, 50, 51, 36, 45, 50, 57, 8, 9, 10, 11, 12, 13, 14, 15, 8, 17, 9, 19, 10, 21, 11, 23, 8, 25, 13, 9, 14, 29, 10, 31, 8, 11, 17, 35, 9, 37, 19, 13, 8, 41, 14, 43, 11, 9, 23, 47, 8, 49, 10, 17, 13, 53, 9, 11, 8, 19, 29, 57, 10, 57, 31, 9, 8, 13, 11, 57, 17, 23, 10
Offset: 1

Views

Author

Robert Price, Aug 24 2017

Keywords

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Programs

  • Mathematica
    u[n_, m_, h_] := (d = Divisors[n]; Min[(h*Ceiling[m/d] - h + 1)*d]); Table[u[n, 8, 8], {n, 1, 70}]

A291497 The arithmetic function uhat(n,1,3).

Original entry on oeis.org

-5, -5, -5, -5, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30, -31, -32, -33, -34, -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45, -46, -47, -48, -49, -50, -51, -52, -53, -54, -55, -56, -57, -58, -59, -60, -61, -62, -63, -64, -65, -66, -67, -68, -69, -70
Offset: 1

Views

Author

Robert Price, Aug 24 2017

Keywords

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Programs

  • Mathematica
    delta[r_, k_, d_] := If[r < k, (k - r)*r - (d - 1), If[k < r && r < d, (d - r)*(r - k) - (d - 1), If[k == r && r == d, d - 1, 0]]] uhat[n_, m_, h_] := (dx = Divisors[n]; dmin = n; For[i = 1, i ≤ Length[dx], i++, d = dx[[i]]; k = m - d*Ceiling[m/d] + d; r = h - d*Ceiling[h/d] + d; If[h ≤ Min[k, d - 1], dmin = Min[dmin, n, (h*Ceiling[m/d] - h + 1)*d, h*m - h*h + 1], dmin = Min[dmin, n, h*m - h*h + 1 - delta[r, k, d]]]]; dmin) Table[uhat[n, 1, 3], {n, 1, 70}]

A291498 The arithmetic function uhat(n,1,4).

Original entry on oeis.org

-11, -11, -11, -11, -11, -12, -14, -16, -18, -20, -22, -24, -26, -28, -30, -32, -34, -36, -38, -40, -42, -44, -46, -48, -50, -52, -54, -56, -58, -60, -62, -64, -66, -68, -70, -72, -74, -76, -78, -80, -82, -84, -86, -88, -90, -92, -94, -96, -98, -100, -102, -104, -106, -108, -110, -112, -114, -116, -118, -120, -122, -124, -126, -128, -130, -132, -134, -136, -138, -140
Offset: 1

Views

Author

Robert Price, Aug 24 2017

Keywords

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Programs

  • Mathematica
    delta[r_, k_, d_] := If[r < k, (k - r)*r - (d - 1), If[k < r && r < d, (d - r)*(r - k) - (d - 1), If[k == r && r == d, d - 1, 0]]] uhat[n_, m_, h_] := (dx = Divisors[n]; dmin = n; For[i = 1, i ≤ Length[dx], i++, d = dx[[i]]; k = m - d*Ceiling[m/d] + d; r = h - d*Ceiling[h/d] + d; If[h ≤ Min[k, d - 1], dmin = Min[dmin, n, (h*Ceiling[m/d] - h + 1)*d, h*m - h*h + 1], dmin = Min[dmin, n, h*m - h*h + 1 - delta[r, k, d]]]]; dmin) Table[uhat[n, 1, 4], {n, 1, 70}]

A291499 The arithmetic function uhat(n,1,5).

Original entry on oeis.org

-19, -19, -19, -19, -19, -19, -21, -24, -27, -30, -33, -36, -39, -42, -45, -48, -51, -54, -57, -60, -63, -66, -69, -72, -75, -78, -81, -84, -87, -90, -93, -96, -99, -102, -105, -108, -111, -114, -117, -120, -123, -126, -129, -132, -135, -138, -141, -144, -147, -150, -153, -156, -159, -162, -165, -168, -171, -174, -177, -180, -183, -186, -189, -192, -195, -198, -201, -204, -207, -210
Offset: 1

Views

Author

Robert Price, Aug 24 2017

Keywords

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Programs

  • Mathematica
    delta[r_, k_, d_] := If[r < k, (k - r)*r - (d - 1), If[k < r && r < d, (d - r)*(r - k) - (d - 1), If[k == r && r == d, d - 1, 0]]] uhat[n_, m_, h_] := (dx = Divisors[n]; dmin = n; For[i = 1, i ≤ Length[dx], i++, d = dx[[i]]; k = m - d*Ceiling[m/d] + d; r = h - d*Ceiling[h/d] + d; If[h ≤ Min[k, d - 1], dmin = Min[dmin, n, (h*Ceiling[m/d] - h + 1)*d, h*m - h*h + 1], dmin = Min[dmin, n, h*m - h*h + 1 - delta[r, k, d]]]]; dmin) Table[uhat[n, 1, 5], {n, 1, 70}]

Formula

Conjectures from Chai Wah Wu, Jun 10 2025: (Start)
a(n) = 2*a(n-1) - a(n-2) for n > 8.
G.f.: x*(-x^7 - 2*x^6 + 19*x - 19)/(x - 1)^2. (End)

A291500 The arithmetic function uhat(n,1,6).

Original entry on oeis.org

-29, -29, -29, -29, -29, -29, -29, -32, -36, -40, -44, -48, -52, -56, -60, -64, -68, -72, -76, -80, -84, -88, -92, -96, -100, -104, -108, -112, -116, -120, -124, -128, -132, -136, -140, -144, -148, -152, -156, -160, -164, -168, -172, -176, -180, -184, -188, -192, -196, -200, -204, -208, -212, -216, -220, -224, -228, -232, -236, -240, -244, -248, -252, -256, -260, -264, -268, -272, -276, -280
Offset: 1

Views

Author

Robert Price, Aug 24 2017

Keywords

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Programs

  • Mathematica
    delta[r_, k_, d_] := If[r < k, (k - r)*r - (d - 1), If[k < r && r < d, (d - r)*(r - k) - (d - 1), If[k == r && r == d, d - 1, 0]]] uhat[n_, m_, h_] := (dx = Divisors[n]; dmin = n; For[i = 1, i ≤ Length[dx], i++, d = dx[[i]]; k = m - d*Ceiling[m/d] + d; r = h - d*Ceiling[h/d] + d; If[h ≤ Min[k, d - 1], dmin = Min[dmin, n, (h*Ceiling[m/d] - h + 1)*d, h*m - h*h + 1], dmin = Min[dmin, n, h*m - h*h + 1 - delta[r, k, d]]]]; dmin) Table[uhat[n, 1, 6], {n, 1, 70}]

A291501 The arithmetic function uhat(n,1,7).

Original entry on oeis.org

-41, -41, -41, -41, -41, -41, -41, -41, -45, -50, -55, -60, -65, -70, -75, -80, -85, -90, -95, -100, -105, -110, -115, -120, -125, -130, -135, -140, -145, -150, -155, -160, -165, -170, -175, -180, -185, -190, -195, -200, -205, -210, -215, -220, -225, -230, -235, -240, -245, -250, -255, -260, -265, -270, -275, -280, -285, -290, -295, -300, -305, -310, -315, -320, -325, -330, -335, -340, -345, -350
Offset: 1

Views

Author

Robert Price, Aug 24 2017

Keywords

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Programs

  • Mathematica
    delta[r_, k_, d_] := If[r < k, (k - r)*r - (d - 1), If[k < r && r < d, (d - r)*(r - k) - (d - 1), If[k == r && r == d, d - 1, 0]]] uhat[n_, m_, h_] := (dx = Divisors[n]; dmin = n; For[i = 1, i ≤ Length[dx], i++, d = dx[[i]]; k = m - d*Ceiling[m/d] + d; r = h - d*Ceiling[h/d] + d; If[h ≤ Min[k, d - 1], dmin = Min[dmin, n, (h*Ceiling[m/d] - h + 1)*d, h*m - h*h + 1], dmin = Min[dmin, n, h*m - h*h + 1 - delta[r, k, d]]]]; dmin) Table[uhat[n, 1, 7], {n, 1, 70}]

A291502 The arithmetic function uhat(n,1,8).

Original entry on oeis.org

-55, -55, -55, -55, -55, -55, -55, -55, -55, -60, -66, -72, -78, -84, -90, -96, -102, -108, -114, -120, -126, -132, -138, -144, -150, -156, -162, -168, -174, -180, -186, -192, -198, -204, -210, -216, -222, -228, -234, -240, -246, -252, -258, -264, -270, -276, -282, -288, -294, -300, -306, -312, -318, -324, -330, -336, -342, -348, -354, -360, -366, -372, -378, -384, -390, -396, -402, -408, -414, -420
Offset: 1

Views

Author

Robert Price, Aug 24 2017

Keywords

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Programs

  • Mathematica
    delta[r_, k_, d_] := If[r < k, (k - r)*r - (d - 1), If[k < r && r < d, (d - r)*(r - k) - (d - 1), If[k == r && r == d, d - 1, 0]]] uhat[n_, m_, h_] := (dx = Divisors[n]; dmin = n; For[i = 1, i ≤ Length[dx], i++, d = dx[[i]]; k = m - d*Ceiling[m/d] + d; r = h - d*Ceiling[h/d] + d; If[h ≤ Min[k, d - 1], dmin = Min[dmin, n, (h*Ceiling[m/d] - h + 1)*d, h*m - h*h + 1], dmin = Min[dmin, n, h*m - h*h + 1 - delta[r, k, d]]]]; dmin) Table[uhat[n, 1, 8], {n, 1, 70}]

Formula

Conjectures from Chai Wah Wu, Jun 10 2025: (Start)
a(n) = 2*a(n-1) - a(n-2) for n > 11.
G.f.: x*(-x^10 - 5*x^9 + 55*x - 55)/(x - 1)^2. (End)

A291509 The arithmetic function uhat(n,2,4).

Original entry on oeis.org

-7, -8, -7, -8, -7, -8, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30, -31, -32, -33, -34, -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45, -46, -47, -48, -49, -50, -51, -52, -53, -54, -55, -56, -57, -58, -59, -60, -61, -62, -63, -64, -65, -66, -67, -68, -69, -70
Offset: 1

Views

Author

Robert Price, Aug 25 2017

Keywords

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Programs

  • Mathematica
    delta[r_, k_, d_] := If[r < k, (k - r)*r - (d - 1), If[k < r && r < d, (d - r)*(r - k) - (d - 1), If[k == r && r == d, d - 1, 0]]] uhat[n_, m_, h_] := (dx = Divisors[n]; dmin = n; For[i = 1, i ≤ Length[dx], i++, d = dx[[i]]; k = m - d*Ceiling[m/d] + d; r = h - d*Ceiling[h/d] + d; If[h ≤ Min[k, d - 1], dmin = Min[dmin, n, (h*Ceiling[m/d] - h + 1)*d, h*m - h*h + 1], dmin = Min[dmin, n, h*m - h*h + 1 - delta[r, k, d]]]]; dmin) Table[uhat[n, 2, 4], {n, 1, 70}]

A291510 The arithmetic function uhat(n,2,5), negated.

Original entry on oeis.org

14, 14, 14, 14, 14, 14, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140
Offset: 1

Views

Author

Robert Price, Aug 25 2017

Keywords

Links

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Programs

  • Mathematica
    delta[r_, k_, d_] := If[r < k, (k - r)*r - (d - 1), If[k < r && r < d, (d - r)*(r - k) - (d - 1), If[k == r && r == d, d - 1, 0]]]; uhat[n_, m_, h_] := (dx = Divisors[n]; dmin = n; For[i = 1, i ≤ Length[dx], i++, d = dx[[i]]; k = m - d*Ceiling[m/d] + d; r = h - d*Ceiling[h/d] + d; If[h ≤ Min[k, d - 1], dmin = Min[dmin, n, (h*Ceiling[m/d] - h + 1)*d, h*m - h*h + 1], dmin = Min[dmin, n, h*m - h*h + 1 - delta[r, k, d]]]]; dmin); Table[uhat[n, 2, 5], {n, 1, 70}]
Previous Showing 81-90 of 113 results. Next

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