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 1-5 of 5 results.

A030159 Numbers n such that in n^3 the parity of digits alternates.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 7, 9, 18, 23, 85, 87, 101, 103, 168, 206, 301, 303, 363, 725, 1683, 2461, 2788, 7921, 9563, 9668, 20606, 28443, 29501, 45168, 46701, 49501, 63556, 78206, 80901, 90009, 167861, 168069, 208288, 278636, 331841, 375121, 440468
Offset: 1

Views

Author

Patrick De Geest

Keywords

Comments

A simple heuristic argument suggests that this sequence (albeit rather sparse) is infinite. The numbers of terms of k digits, for k=1..14, are 8, 4, 8, 6, 10, 14, 20, 18, 33, 23, 42, 37, 46, 77, respectively. The 5 numbers obtained multiplying the first h=1..5 terms of (1+10^2, 1+10^8, 1+10^32, 1+10^128, 1+10^512), are all member of the sequence. The largest one is a number of 683 digits whose alternating cube has 2047 digits. - Giovanni Resta, Aug 16 2018

Links

Crossrefs

Cf. A030160, A030161, A030162, A030151.

Programs

  • Mathematica
    n3pdaQ[n_]:=Module[{pty=Boole[EvenQ/@IntegerDigits[n^3]],len= IntegerLength[ n^3]}, pty== PadRight[{},len,{1,0}]||pty==PadRight[ {}, len, {0,1}]]; Join[{0},Select[Range[450000],n3pdaQ]] (* Harvey P. Dale, Mar 26 2018 *)

A297644 Pentagonal numbers (A000326) in which parity of digits alternates.

Original entry on oeis.org

1, 5, 12, 70, 92, 145, 210, 852, 925, 2147, 2501, 3290, 3432, 3876, 4187, 4347, 6305, 6501, 12105, 12927, 25676, 27270, 27676, 45850, 58707, 69230, 69876, 70525, 76501, 78547, 98945, 101270, 123410, 161212, 270725, 349692, 367290, 567030, 707610, 709672
Offset: 1

Views

Author

Colin Barker, Jan 02 2018

Keywords

Comments

Intersection of A000326 and A030141. - Felix Fröhlich, Jan 03 2018

Examples

			3876 is in the sequence because 3, 8, 7 and 6 have odd and even parity alternately.

Links

Crossrefs

Cf. A297645, A297646, A297647.
Cf. A000326, A030141, A030152, A030160, A068882.

Programs

  • Maple
    filter:= proc(n) local L;
  if n < 10 then return true fi;
  L:= convert(n, base, 10) mod 2;
  not has(L[2..-1]-L[1..-2], 0)
end proc:
select(filter, [seq(n*(3*n-1)/2, n=1..1000)]); # Robert Israel, Jan 03 2018
  • PARI
    is_alt(n) = m=n; e=n%10; n\=10; while(n>0, f=n%10; if(e%2==f%2, return, e=f; n\=10)); return(m)
select(is_alt, vector(1000, n, (3*n^2-n)/2))

A297645 Hexagonal numbers (A000384) in which parity of digits alternates.

Original entry on oeis.org

1, 6, 45, 276, 325, 496, 561, 630, 703, 2145, 2701, 6903, 8385, 10585, 14365, 18721, 25878, 38503, 47278, 74305, 89676, 90525, 107416, 109278, 147696, 149878, 210925, 254541, 303810, 345696, 349030, 383250, 454581, 527878, 561270, 674541, 705078, 709836
Offset: 1

Views

Author

Colin Barker, Jan 02 2018

Keywords

Comments

Intersection of A000384 and A030141. - Felix Fröhlich, Jan 03 2018

Examples

			6903 is in the sequence because 6, 9, 0 and 3 have even and odd parity alternately.

Links

Crossrefs

Cf. A297644, A297646, A297647.
Cf. A000384, A030141, A030152, A030160, A068882.

Programs

  • Maple
    filter:= proc(n) local L;
  if n < 10 then return true fi;
  L:= convert(n, base, 10) mod 2;
  not has(L[2..-1]-L[1..-2], 0)
end proc:
select(filter, [seq(n*(2*n-1),n=1..10^4)]); # Robert Israel, Jan 05 2018
  • PARI
    is_alt(n) = m=n; e=n%10; n\=10; while(n>0, f=n%10; if(e%2==f%2, return, e=f; n\=10)); return(m)
select(is_alt, vector(1000, n, (4*n^2-2*n)/2))

A297646 Heptagonal numbers (A000566) in which parity of digits alternates.

Original entry on oeis.org

1, 7, 18, 34, 81, 189, 616, 783, 874, 3010, 4141, 4347, 5452, 6943, 8323, 12145, 14707, 18361, 52345, 69472, 74563, 78943, 96727, 129618, 147258, 163456, 214183, 232105, 250747, 258727, 270109, 276723, 278389, 307476, 309232, 381616, 389470, 436183, 450925
Offset: 1

Views

Author

Colin Barker, Jan 02 2018

Keywords

Comments

Intersection of A000566 and A030141. - Felix Fröhlich, Jan 03 2018

Examples

			6943 is in the sequence because 6, 9, 4 and 3 have even and odd parity alternately.

Links

Crossrefs

Cf. A297644, A297645, A297647.
Cf. A000566, A030141, A030152, A030160, A068882.

Programs

  • Mathematica
    Join[{1,7},Select[PolygonalNumber[7,Range[1000]],Union[Abs[Differences[ Boole[ OddQ[ IntegerDigits[ #]]]]]] =={1}&]] (* Harvey P. Dale, Jul 14 2022 *)
  • PARI
    is_alt(n) = m=n; e=n%10; n\=10; while(n>0, f=n%10; if(e%2==f%2, return, e=f; n\=10)); return(m)
select(is_alt, vector(1000, n, (5*n^2-3*n)/2))

A297647 Octagonal numbers (A000567) in which parity of digits alternates.

Original entry on oeis.org

1, 8, 21, 65, 96, 341, 3816, 4961, 8321, 8965, 9296, 10325, 12545, 14145, 14981, 16725, 18565, 23056, 27456, 36741, 63656, 65416, 103416, 105656, 169456, 181056, 210145, 216545, 232965, 236321, 256961, 412181, 430165, 434721, 569416, 614721, 658945, 698901
Offset: 1

Views

Author

Colin Barker, Jan 02 2018

Keywords

Comments

Intersection of A000567 and A030141. - Felix Fröhlich, Jan 03 2018

Examples

			8321 is in the sequence because 8, 3, 2 and 1 have even and odd parity alternately.

Links

Crossrefs

Cf. A297644, A297645, A297646.
Cf. A000567, A030141, A030152, A030160, A068882.

Programs

  • Maple
    filter:= proc(n) local L;
  if n < 10 then return true fi;
  L:= convert(n,base,10) mod 2;
  not has(L[2..-1]-L[1..-2],0)
end proc:
select(filter, [seq(n*(3*n-2),n=1..1000)]); # Robert Israel, Jan 03 2018
  • PARI
    is_alt(n) = m=n; e=n%10; n\=10; while(n>0, f=n%10; if(e%2==f%2, return, e=f; n\=10)); return(m)
select(is_alt, vector(1000, n, (6*n^2-4*n)/2))
Showing 1-5 of 5 results.

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