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 A285845 Powers (A001597) that are also cyclops numbers (A134808). 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 31 23:09 EDT 2023. Contains 363068 sequences. (Running on oeis4.)