A285845 Powers (A001597) that are also cyclops numbers (A134808).

11025, 19044, 21025, 24025, 32041, 38025, 42025, 47089, 51076, 58081, 59049, 65025, 66049, 67081, 74088, 75076, 87025, 93025, 1110916, 1140624, 1170724, 1190281, 1240996, 1270129, 1290496, 1340964, 1350244, 1380625, 1420864, 1430416, 1490841, 1510441

Offset

1,1

Comments

The first term not in A160711 is 74088 = 42^3.

Intersection of A001597 and A134808. - Robert G. Wilson v, Apr 27 2017

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1156 terms from Robert G. Wilson v)

Mathematica

Select[NestList[If[# == 1, 4, Min@ Table[(Floor[#^(1/k)] + 1)^k, {k, 2, 1 + Floor@ Log2@ #}]] &, 1, 1400], Function[n, And[OddQ@ Length@ #, #[[ Ceiling[Length[#]/2] ]] == 0, DigitCount[n, 10, 0] == 1] &@ IntegerDigits@ n]] (* Michael De Vlieger, Apr 27 2017, after Robert G. Wilson v at A001597 *)
cyclopsQ[n_Integer, b_: 10] := Module[{digitList = IntegerDigits[n, b], len, pos0s, flag}, len = Length[digitList]; pos0s = Select[Range[len], digitList[[#]] == 0 &]; flag = OddQ[len] && (Length[pos0s] == 1) && (pos0s == {(len + 1)/2}); Return[flag]]; (* from Alonso del Arte in A134808 *) min = 0; max = 1520000; t = Union@ Flatten@ Table[n^expo, {expo, Prime@ Range@ PrimePi@ Log2@ max}, {n, Floor[1 + min^(1/expo)], max^(1/expo)}]; Select[t, cyclopsQ] (* Robert G. Wilson v, Apr 27 2017 *)

Prog

(PARI)
is_cyclops(k) = {
  if(k==0, return(1));
  my(d=digits(k), j);
  if(#d%2==0 || d[#d\2+1]!=0, return(0));
  for(j=1, #d\2, if(d[j]==0, return(0)));
  for(j=#d\2+2, #d, if(d[j]==0, return(0)));
  return(1)}
L=List(); for(n=1, 100000, if(ispower(n) && is_cyclops(n), listput(L, n))); Vec(L)

Crossrefs

Cf. A001597, A134808, A160711.

Sequence in context: A218598 A096930 A233720 * A160711 A129087 A239828

Adjacent sequences: A285842 A285843 A285844 * A285846 A285847 A285848

Keyword

nonn,base

Author

Colin Barker, Apr 27 2017

Status

approved