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 1-4 of 4 results.

A160711 Cyclops squares: squares (A000290) that are also cyclops numbers (A134808).

Original entry on oeis.org

0, 11025, 19044, 21025, 24025, 32041, 38025, 42025, 47089, 51076, 58081, 59049, 65025, 66049, 67081, 75076, 87025, 93025, 1110916, 1140624, 1170724, 1190281, 1240996, 1270129, 1290496, 1340964, 1350244, 1380625, 1420864, 1430416
Offset: 1

Views

Author

Omar E. Pol, Jun 08 2009

Keywords

Examples

			19044 is in the sequence because it is a square (138^2) and is also a cyclops number (odd number of digits, middle digit is the only zero).
11025 is in the sequence because it is a square (105^2) and is also a cyclops number (odd number of digits, middle digit is the only zero). - _Michael B. Porter_, Jul 09 2016

Links

Crossrefs

Cf. A000290, A134808, A134809, A134148, A138131, A153806, A160712, A160717, A239828.

Programs

  • Mathematica
    Select[Range[0, 1200]^2, And[OddQ@ Length@ #, #[[Ceiling[Length[#]/2]]] == 0, Count[#, 0] == 1] &@ IntegerDigits@ # &] (* Michael De Vlieger, Jul 08 2016 *)
cnQ[n_]:=Module[{len=IntegerLength[n]},OddQ[len]&&DigitCount[n,10,0]==1 && IntegerDigits[n][[(len+1)/2]]==0]; Join[{0},Select[Range[1200]^2,cnQ]] (* Harvey P. Dale, Mar 19 2018 *)

A160717 Cyclops triangular numbers.

Original entry on oeis.org

0, 105, 406, 703, 903, 11026, 13041, 14028, 15051, 27028, 36046, 41041, 43071, 46056, 61075, 66066, 75078, 77028, 83028, 85078, 93096, 1110795, 1130256, 1160526, 1180416, 1250571, 1290421, 1330896, 1350546, 1360425, 1380291
Offset: 1

Views

Author

Omar E. Pol, Jun 08 2009

Keywords

Comments

Triangular numbers (A000217) that are also cyclops numbers (A134808).

Examples

			105 is in the sequence since it is both a triangular number (105 = 1 + 2 + ... + 14) and a Cyclops number (number of digits is odd, and the only zero is the middle digit). - _Michael B. Porter_, Jul 08 2016

Links

Crossrefs

Cf. A000217, A134808, A134809, A138131, A138148, A153806, A160711, A160712.

Programs

  • Maple
    count:= 1: A[1]:= 0:
for d from 1 to 3 do
  for x from 0 to 9^d-1 do
    L:= convert(x+9^d,base,9);
    X:= add((L[i]+1)*10^(i-1),i=1..d);
    for y from 0 to 9^d-1 do
      L:= convert(y+9^d,base,9);
      Y:= add((L[i]+1)*10^(i-1),i=1..d);
      Z:= Y + 10^(d+1)*X;
      if issqr(1+8*Z) then
        count:= count+1;
        A[count]:= Z;
      fi
od od od:
seq(A[i],i=1..count); # Robert Israel, Jul 08 2016
  • Mathematica
    cyclopsQ[n_] := Block[{id=IntegerDigits@n,lg=Floor[Log[10,n]+1]}, Count[id,0]==1 && OddQ@lg && id[[(lg+1)/2]]==0]; lst = {0}; Do[t = n (n + 1)/2; If[ cyclopsQ@t, AppendTo[lst, t]], {n, 0, 1670}]; lst (* Robert G. Wilson v, Jun 09 2009 *)
cyclpsQ[n_]:=With[{len=IntegerLength[n]},OddQ[len]&&DigitCount[n,10,0]==1&&IntegerDigits[n][[(len+1)/2]]==0]; Join[{0},Select[ Accumulate[ Range[2000]],cyclpsQ]] (* Harvey P. Dale, Nov 05 2024 *)

Extensions

More terms from Robert G. Wilson v, Jun 09 2009
Offset and b-file changed by N. J. A. Sloane, Jul 27 2016

A160725 Cyclops semiprimes.

Original entry on oeis.org

106, 201, 202, 203, 205, 206, 209, 301, 302, 303, 305, 309, 403, 407, 501, 502, 505, 703, 706, 707, 802, 803, 807, 901, 905, 11013, 11014, 11015, 11017, 11019, 11021, 11023, 11029, 11031, 11035, 11038, 11041, 11042, 11051, 11053
Offset: 1

Views

Author

Omar E. Pol, Jun 12 2009

Keywords

Comments

Cyclops numbers (A134808) that are also semiprimes (A001358).

Links

Crossrefs

Cf. A001358, A134808, A134809, A138131, A138148, A153806, A153807, A160711, A160712, A160717.

Programs

  • Maple
    g:= proc(x,n)
  local L,i;
  L:= convert(x+9^(2*n),base,9);
  add((L[i]+1)*10^(i-1),i=1..n)+add((L[i]+1)*10^i,i=n+1..2*n)
end proc:
select(t -> numtheory:-bigomega(t)=2,[seq(seq(g(i,n),i=0..9^(2*n)-1),n=1..2)]); # Robert Israel, Jan 20 2019
  • Mathematica
    Select[Range@ 12000, And[OddQ@ #2, #3[[Ceiling[#2/2] ]] == 0, Count[#3, 0] == 1, PrimeOmega@ #1 == 2] & @@ {#, IntegerLength@ #, IntegerDigits@ #} &] (* or *)
Select[Flatten@ Table[a (10^(d + 1)) + b, {d, 2}, {a, FromDigits /@ Tuples[Range@ 9, {d}]}, {b, FromDigits /@ Tuples[Range@ 9, {d}]}], PrimeOmega@ # == 2 &] (* Michael De Vlieger, Jan 20 2019 *)

A183057 Cyclops emirps.

Original entry on oeis.org

107, 701, 709, 907, 11057, 11071, 11083, 12071, 12073, 13043, 14029, 14057, 14071, 14081, 14087, 15013, 15053, 15091, 16063, 16073, 17011, 17021, 17033, 17041, 17047, 18013, 18041, 18077, 18089, 19013, 19037, 19051, 31033, 31051, 31063, 31069, 31081, 31091, 32077, 32099
Offset: 1

Views

Author

Omar E. Pol, Dec 21 2010

Keywords

Comments

Intersection of emirps A006567 and cyclops numbers A134808.
The smallest cyclops emirp 107 was mentioned by Patrick Capelle in Prime Curios! (see link).

Examples

			a(1) = 107 is in the sequence because 107 is an emirp A006567 and it is also a cyclops number A134808.

Links

Crossrefs

Cf. A006567, A134808, A134809, A138148, A160712, A160725.

Formula

A006567 INTERSECT A134808.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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