A026098 -id:A026098 - cp's OEIS frontend

A026100 a(n) = number of the column of A026098 that contains n.

1, 2, 1, 3, 1, 2, 1, 4, 3, 2, 1, 4, 1, 2, 3, 5, 1, 5, 1, 4, 3, 2, 1, 6, 5, 2, 6, 4, 1, 7, 1, 8, 3, 2, 5, 7, 1, 2, 3, 6, 1, 6, 1, 4, 7, 9, 1, 8, 7, 8, 3, 4, 1, 9, 5, 10, 3, 2, 1, 9, 1, 11, 8, 12, 5, 6, 1, 4, 2, 9, 1, 10, 1, 2, 10, 4, 7, 6, 1, 11, 11, 13, 1, 10, 5, 14, 3, 8, 1, 12, 7, 3, 2, 15, 5, 13, 1, 11, 9, 12

Offset: 1

Clark Kimberling

Antti Karttunen, Table of n, a(n) for n = 1..19477

Cf. A026098.

getrow(n, all) = {if (n==1, return ([1])); if (n==2, return ([3, 2])); my(row = vector(n)); row[1] = prime(n); for (k=2, n, my(ok = 0, m = 1, val); until(ok, val = m*prime(n+1-k); if (!setsearch(all, val) && !setsearch(Set(row), val), ok = 1); m++; ); row[k] = val; ); return (row); };
A026100list(up_to_row) = { my(all = [], m = Map(), lista = List([]), u); for(n=1, up_to_row, my(row = getrow(n, all)); for(k=1, n, mapput(m,row[k],k)); all = Set(concat(all, row))); for(n=1,oo,if(mapisdefined(m,n,&u), listput(lista,u), if(isprime(n)&&(n>2),listput(lista,1), return(Vec(lista))))); };
v026100 = A026100list(1200);
A026100(n) = v026100[n]; \\ Antti Karttunen, Jan 18 2020, after program in A026098 provided by Michel Marcus.

a(27) onward corrected by Sean A. Irvine, Sep 15 2019

A070264 Inverse permutation to that in A026098.

Original entry on oeis.org

1, 3, 2, 6, 4, 5, 7, 10, 9, 8, 11, 14, 16, 12, 13, 15, 22, 20, 29, 19, 18, 17, 37, 21, 26, 23, 27, 25, 46, 28, 56, 36, 24, 30, 33, 35, 67, 38, 31, 34, 79, 42, 92, 32, 43, 45, 106, 44, 52, 53, 39, 40, 121, 54, 41, 55, 48, 57, 137, 64, 154, 66, 63, 78, 50, 51, 172, 49, 47, 75

Offset: 1

Antti Karttunen, May 07 2002

Index entries for sequences that are permutations of the natural numbers

More terms from David Wasserman, Aug 12 2002

A026099 Row of A026098 that contains n.

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 5, 5, 5, 7, 6, 8, 6, 6, 6, 9, 6, 7, 7, 7, 7, 10, 7, 11, 8, 7, 8, 8, 8, 12, 9, 8, 8, 13, 9, 14, 8, 9, 9, 15, 9, 10, 10, 9, 9, 16, 10, 9, 10, 10, 11, 17, 11, 18, 11, 11, 12, 10, 10, 19, 10, 10, 12, 20, 11, 21, 13, 12, 11, 11, 11, 22, 13, 12, 13, 23, 13, 11, 14, 12, 12, 24, 13, 12, 11, 12, 15, 12, 14, 25, 14, 13, 14

Offset: 1

Clark Kimberling

nonn

a(24) onward corrected by Sean A. Irvine, Sep 15 2019

A026101 T(n,1) + T(n,2) + ... T(n,n), where T is the array in A026098.

Original entry on oeis.org

1, 5, 15, 34, 68, 118, 186, 279, 400, 563, 754, 998, 1265, 1614, 2015, 2468, 3023, 3610, 4277, 4980, 5795, 6734, 7754, 8847, 10170, 11502, 13002, 14661, 16373, 18150, 20212, 22351, 24465, 26949, 29608, 32312, 35295, 38459, 41644, 45192, 48910, 52858, 56965, 61291, 65677

Offset: 1

Clark Kimberling

nonn

a(6) onward corrected by Sean A. Irvine, Sep 15 2019

A026102 a(n) = T(2n-1,n), where T is the array in A026098.

Original entry on oeis.org

1, 6, 15, 28, 55, 78, 119, 152, 230, 290, 372, 444, 574, 645, 752, 901, 1062, 1159, 1273, 1491, 1606, 1817, 1992, 2314, 2522, 2828, 2987, 3210, 3270, 3616, 4191, 4323, 4658, 5004, 5364, 5738, 6123, 6357, 6847, 7266, 7697, 7964, 8595, 8685, 9259, 9552, 10339, 10927, 11577, 11908

Offset: 1

Clark Kimberling

nonn

Cf. A001844, A026098.

Cf. A033286. [R. J. Mathar, Oct 22 2008]

T[1, 1] = 1; T[2, 1] = 3; T[2, 2] = 2; T[n_, 1] := Prime[n];
T[n_, k_] := T[n, k] = Module[{m, mp, jtt}, For[m = 1, True, m++, mp = m Prime[n+1-k]; jtt = Join[Table[T[i, j], {i, 1, n-1}, {j, 1, i}] // Flatten, Table[T[n, j], {j, 1, k-1}]]; If[FreeQ[jtt, mp], Return[mp]]]];
a[n_] := T[2n-1, n]; (* Jean-François Alcover, Sep 05 2019 *)

lista(nn) = {my(all = []); for (n=1, nn, my(row = getrow(n, all)); if (n % 2, print1(row[(n+1)/2], ", ")); all = Set(concat(all, row)););} \\ uses getrow from A026098; Michel Marcus, Sep 04 2019

a(n) = A026098(A001844(n)). - Sean A. Irvine, Sep 16 2019

Corrected and extended by Michel Marcus, Sep 04 2019

A026103 a(n) = T(n,1) + T(n-1,2) + ...+ T(n-k+1,k), where k = floor((n+1)/2) and T is the array defined in A026098.

Original entry on oeis.org

1, 3, 7, 13, 25, 36, 62, 78, 126, 152, 244, 266, 419, 423, 637, 679, 932, 1007, 1307, 1419, 1697, 1918, 2229, 2514, 2899, 3300, 3672, 4223, 4663, 5298, 5682, 6495, 6988, 7619, 8324, 9289, 9861, 11033, 11697, 12812, 13727, 14956, 16008, 17298, 18473, 19701, 21186, 22502

Offset: 1

Clark Kimberling

nonn

a(n) is the sum of the terms of the n-th antidiagonal of triangle A026098. - Sean A. Irvine, Sep 16 2019

a(11) onward corrected and more terms from Sean A. Irvine, Sep 16 2019

A026104 a(n) = greatest number in row n of A026098 that is not a positive power of 2.

Original entry on oeis.org

1, 3, 6, 10, 15, 24, 33, 44, 55, 69, 92, 115, 138, 161, 186, 217, 248, 287, 328, 369, 410, 451, 492, 533, 590, 649, 708, 767, 826, 885, 944, 1003, 1068, 1157, 1246, 1335, 1424, 1515, 1616, 1717, 1818, 1919, 2020, 2121, 2222, 2323, 2424, 2540, 2667, 2794, 2921

Offset: 1

Clark Kimberling

nonn

Corrected and extended by David Wasserman, Aug 12 2002

cp's OEIS Frontend

A026100 a(n) = number of the column of A026098 that contains n.

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A070264 Inverse permutation to that in A026098.

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A026099 Row of A026098 that contains n.

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A026101 T(n,1) + T(n,2) + ... T(n,n), where T is the array in A026098.

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A026102 a(n) = T(2n-1,n), where T is the array in A026098.

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PARI

Formula

Extensions

A026103 a(n) = T(n,1) + T(n-1,2) + ...+ T(n-k+1,k), where k = floor((n+1)/2) and T is the array defined in A026098.

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A026104 a(n) = greatest number in row n of A026098 that is not a positive power of 2.

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Extensions