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 1-9 of 9 results.

A045809 9-ish numbers (end in 13, 37, 59, 91).

Original entry on oeis.org

13, 37, 59, 91, 113, 137, 159, 191, 213, 237, 259, 291, 313, 337, 359, 391, 413, 437, 459, 491, 513, 537, 559, 591, 613, 637, 659, 691, 713, 737, 759, 791, 813, 837, 859, 891, 913, 937, 959, 991, 1013, 1037, 1059, 1091, 1113, 1137, 1159, 1191, 1213, 1237
Offset: 1

Views

Author

J. H. Conway

Keywords

Links

Crossrefs

Cf. A045800-A045808, A045572, A045797, A045798.

Programs

  • Haskell
    import Data.List (findIndices)
a045809 n = a045809_list !! (n-1)
a045809_list = findIndices (`elem` [13,37,59,91]) $ cycle [0..99]
-- Reinhard Zumkeller, Jan 23 2012
  • Mathematica
    CoefficientList[Series[(13 + 24*x + 22*x^2 + 32*x^3 + 9*x^4)/(1 - x - x^4 + x^5), {x, 0, 80}], x] (* Wesley Ivan Hurt, Jan 23 2017 *)
LinearRecurrence[{1,0,0,1,-1},{13,37,59,91,113},50] (* Harvey P. Dale, Feb 03 2024 *)

Formula

G.f.: x*(13+24*x+22*x^2+32*x^3+9*x^4)/(1-x-x^4+x^5). - Colin Barker, Jan 23 2012
a(n) = (50*n+4*i^(n*(n-1))+3*(-1)^n-25)/2, where i=sqrt(-1). - Bruno Berselli, Feb 22 2012

Extensions

More terms from Erich Friedman.

A045801 1-ish numbers (end in 11, 39, 73, 77).

Original entry on oeis.org

11, 39, 73, 77, 111, 139, 173, 177, 211, 239, 273, 277, 311, 339, 373, 377, 411, 439, 473, 477, 511, 539, 573, 577, 611, 639, 673, 677, 711, 739, 773, 777, 811, 839, 873, 877, 911, 939, 973, 977, 1011, 1039, 1073, 1077, 1111, 1139, 1173, 1177, 1211, 1239
Offset: 1

Views

Author

J. H. Conway

Keywords

Links

Crossrefs

Cf. A045800-A045809, A045572, A045797, A045798.

Programs

  • Haskell
    import Data.List (findIndices)
a045801 n = a045801_list !! (n-1)
a045801_list = findIndices (`elem` [11,39,73,77]) $ cycle [0..99]
-- Reinhard Zumkeller, Jan 23 2012
  • Mathematica
    Table[100n+k,{n,0,20},{k,{11,39,73,77}}]//Flatten (* or *) LinearRecurrence[ {1,0,0,1,-1},{11,39,73,77,111},80] (* Harvey P. Dale, Jul 05 2019 *)

Formula

G.f.: x*(11+28*x+34*x^2+4*x^3+23*x^4)/(1-x-x^4+x^5). - Colin Barker, Jan 23 2012
a(n) = (50*n-12*i^(n*(n-1))-9*(-1)^n-25)/2, where i=sqrt(-1). - Bruno Berselli, Feb 23 2012

Extensions

More terms from Erich Friedman.

A045808 8-ish numbers (end in 67, 69, 81, 83).

Original entry on oeis.org

67, 69, 81, 83, 167, 169, 181, 183, 267, 269, 281, 283, 367, 369, 381, 383, 467, 469, 481, 483, 567, 569, 581, 583, 667, 669, 681, 683, 767, 769, 781, 783, 867, 869, 881, 883, 967, 969, 981, 983, 1067, 1069, 1081, 1083, 1167, 1169, 1181, 1183, 1267, 1269
Offset: 1

Views

Author

J. H. Conway

Keywords

Links

Crossrefs

Cf. A045800-A045809.
Cf. A045572, A045797, A045798.

Programs

  • Haskell
    import Data.List (findIndices)
a045808 n = a045808_list !! (n-1)
a045808_list = findIndices (`elem` [67,69,81,83]) $ cycle [0..99]
-- Reinhard Zumkeller, Jan 23 2012
  • Mathematica
    Select[Range[1300],MemberQ[{67,69,81,83},Mod[#,100]]&] (* Harvey P. Dale, Jul 03 2013 *)

Formula

Empirical g.f.: x*(67+2*x+12*x^2+2*x^3+17*x^4)/(1-x-x^4+x^5). - Colin Barker, Jan 23 2012

Extensions

More terms from Erich Friedman

A045802 2-ish numbers (end in 03, 21, 29, 47).

Original entry on oeis.org

3, 21, 29, 47, 103, 121, 129, 147, 203, 221, 229, 247, 303, 321, 329, 347, 403, 421, 429, 447, 503, 521, 529, 547, 603, 621, 629, 647, 703, 721, 729, 747, 803, 821, 829, 847, 903, 921, 929, 947, 1003, 1021, 1029, 1047, 1103, 1121, 1129, 1147, 1203, 1221
Offset: 1

Views

Author

J. H. Conway

Keywords

Links

Crossrefs

Cf. A045800-A045809, A045572, A045797, A045798.

Programs

  • Haskell
    import Data.List (findIndices)
a045802 n = a045802_list !! (n-1)
a045802_list = findIndices (`elem` [3,21,29,47]) $ cycle [0..99]
-- Reinhard Zumkeller, Jan 23 2012
  • Mathematica
    Join[{3},Select[Range[10,1300],MemberQ[{{0,3},{2,1},{2,9},{4,7}}, Take[ IntegerDigits[#],-2]]&]] (* or *) LinearRecurrence[{1,0,0,1,-1},{3,21,29,47,103},50] (* Harvey P. Dale, May 05 2012 *)

Formula

G.f.: x*(3+18*x+8*x^2+18*x^3+53*x^4)/(1-x-x^4+x^5). - Colin Barker, Jan 23 2012
a(n) = (50*n-24*i^(n*(n+1))-7*(-1)^n-75)/2, where i=sqrt(-1). - Bruno Berselli, Feb 23 2012
a(1)=3, a(2)=21, a(3)=29, a(4)=47, a(5)=103, a(n)=a(n-1)+a(n-4)-a(n-5) .[Harvey P. Dale, May 05 2012]

Extensions

More terms from Erich Friedman.

A045803 3-ish numbers (end in 17, 19, 31, 33).

Original entry on oeis.org

17, 19, 31, 33, 117, 119, 131, 133, 217, 219, 231, 233, 317, 319, 331, 333, 417, 419, 431, 433, 517, 519, 531, 533, 617, 619, 631, 633, 717, 719, 731, 733, 817, 819, 831, 833, 917, 919, 931, 933, 1017, 1019, 1031, 1033, 1117, 1119, 1131, 1133, 1217, 1219
Offset: 1

Views

Author

J. H. Conway

Keywords

Links

Crossrefs

Cf. A045800-A045809.
Cf. A045572, A045797, A045798.

Programs

  • Haskell
    import Data.List (findIndices)
a045803 n = a045803_list !! (n-1)
a045803_list = findIndices (`elem` [17,19,31,33]) $ cycle [0..99]
-- Reinhard Zumkeller, Jan 23 2012
  • Mathematica
    Select[Range[1300],MemberQ[{17,19,31,33},Mod[#,100]]&] (* or *) LinearRecurrence[{1,0,0,1,-1},{17,19,31,33,117},50] (* Harvey P. Dale, Dec 17 2014 *)
  • PARI
    a(n) = -75/2 - (23*(-1)^n)/2 - (9-9*I)*(-I)^n - (9+9*I)*I^n + 25*n \\ Colin Barker, Oct 16 2015
  • PARI
    Vec(x*(17+2*x+12*x^2+2*x^3+67*x^4)/(1-x-x^4+x^5) + O(x^100)) \\ Colin Barker, Oct 16 2015

Formula

G.f.: x*(17+2*x+12*x^2+2*x^3+67*x^4)/(1-x-x^4+x^5). - Colin Barker, Jan 23 2012
a(n) = -75/2 - (23*(-1)^n)/2 - (9-9*i)*(-i)^n - (9+9*i)*i^n + 25*n where i=sqrt(-1). - Colin Barker, Oct 16 2015

Extensions

More terms from Erich Friedman

A045804 4-ish numbers (end in 09, 41, 63, 87).

Original entry on oeis.org

9, 41, 63, 87, 109, 141, 163, 187, 209, 241, 263, 287, 309, 341, 363, 387, 409, 441, 463, 487, 509, 541, 563, 587, 609, 641, 663, 687, 709, 741, 763, 787, 809, 841, 863, 887, 909, 941, 963, 987, 1009, 1041, 1063, 1087, 1109, 1141, 1163, 1187, 1209, 1241
Offset: 1

Views

Author

J. H. Conway

Keywords

Links

Crossrefs

Cf. A045800-A045809.
Cf. A045572, A045797, A045798.

Programs

  • Haskell
    import Data.List (findIndices)
a045804 n = a045804_list !! (n-1)
a045804_list = findIndices (`elem` [9,41,63,87]) $ cycle [0..99]
-- Reinhard Zumkeller, Jan 23 2012
  • Mathematica
    Select[Range[1250],MemberQ[{9,41,63,87},Mod[#,100]]&] (* Harvey P. Dale, Aug 01 2020 *)

Formula

G.f.: x*(9+32*x+22*x^2+24*x^3+13*x^4)/(1-x-x^4+x^5). - Colin Barker, Jan 23 2012

Extensions

More terms from Erich Friedman.

A045805 5-ish numbers (end in 51, 57, 93, 99).

Original entry on oeis.org

51, 57, 93, 99, 151, 157, 193, 199, 251, 257, 293, 299, 351, 357, 393, 399, 451, 457, 493, 499, 551, 557, 593, 599, 651, 657, 693, 699, 751, 757, 793, 799, 851, 857, 893, 899, 951, 957, 993, 999, 1051, 1057, 1093, 1099, 1151, 1157, 1193, 1199, 1251, 1257
Offset: 1

Views

Author

J. H. Conway

Keywords

Links

Crossrefs

Cf. A045800-A045809.
Cf. A045572, A045797, A045798.

Programs

  • Haskell
    import Data.List (findIndices)
a045805 n = a045805_list !! (n-1)
a045805_list = findIndices (`elem` [51,57,93,99]) $ cycle [0..99]
-- Reinhard Zumkeller, Jan 23 2012
  • Mathematica
    Select[Range[50,1500],MemberQ[{51,57,93,99},Mod[#,100]]&] (* Harvey P. Dale, Nov 14 2022 *)

Formula

Empirical g.f.: x*(51+6*x+36*x^2+6*x^3+x^4)/(1-x-x^4+x^5). - Colin Barker, Jan 23 2012

Extensions

More terms from Erich Friedman

A045806 6-ish numbers (end in 23, 27, 61, 89).

Original entry on oeis.org

23, 27, 61, 89, 123, 127, 161, 189, 223, 227, 261, 289, 323, 327, 361, 389, 423, 427, 461, 489, 523, 527, 561, 589, 623, 627, 661, 689, 723, 727, 761, 789, 823, 827, 861, 889, 923, 927, 961, 989, 1023, 1027, 1061, 1089, 1123, 1127, 1161, 1189, 1223, 1227
Offset: 1

Views

Author

J. H. Conway

Keywords

Links

Crossrefs

Cf. A045800-A045809.
Cf. A045572, A045797, A045798.

Programs

  • Haskell
    import Data.List (findIndices)
a045806 n = a045806_list !! (n-1)
a045806_list = findIndices (`elem` [23,27,61,89]) $ cycle [0..99]
-- Reinhard Zumkeller, Jan 23 2012

Formula

Empirical g.f.: x*(23+4*x+34*x^2+28*x^3+11*x^4)/(1-x-x^4+x^5). - Colin Barker, Jan 23 2012

Extensions

More terms from Erich Friedman

A045807 7-ish numbers (end in 53, 71, 79, 97).

Original entry on oeis.org

53, 71, 79, 97, 153, 171, 179, 197, 253, 271, 279, 297, 353, 371, 379, 397, 453, 471, 479, 497, 553, 571, 579, 597, 653, 671, 679, 697, 753, 771, 779, 797, 853, 871, 879, 897, 953, 971, 979, 997, 1053, 1071, 1079, 1097, 1153, 1171, 1179, 1197, 1253, 1271
Offset: 1

Views

Author

J. H. Conway

Keywords

Links

Crossrefs

Cf. A045800-A045809.
Cf. A045572, A045797, A045798.

Programs

  • Haskell
    import Data.List (findIndices)
a045807 n = a045807_list !! (n-1)
a045807_list = findIndices (`elem` [53,71,79,97]) $ cycle [0..99]
-- Reinhard Zumkeller, Jan 23 2012

Formula

Empirical g.f.: x*(53+18*x+8*x^2+18*x^3+3*x^4)/(1-x-x^4+x^5). - Colin Barker, Jan 23 2012

Extensions

More terms from Erich Friedman
Showing 1-9 of 9 results.

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