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URL: https://oeis.org/A274765

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A274765
Cyclops numbers with circular digits {0,6,8,9}.
2
0, 606, 608, 609, 806, 808, 809, 906, 908, 909, 66066, 66068, 66069, 66086, 66088, 66089, 66096, 66098, 66099, 68066, 68068, 68069, 68086, 68088, 68089, 68096, 68098, 68099, 69066, 69068, 69069, 69086, 69088, 69089, 69096, 69098, 69099, 86066, 86068, 86069, 86086, 86088, 86089, 86096, 86098, 86099
OFFSET
1,2
COMMENTS
Intersection of A001743 and A134808.
EXAMPLE
86069 is a member because it is cyclops (A134808) and each digit contains at least one loop (A001743).
MATHEMATICA
cncdQ[n_]:=Module[{idn=IntegerDigits[n]}, OddQ[Length[idn]]&&Count[idn, 0] == 1&&idn[[(Length[idn]+1)/2]]==0&&SubsetQ[{0, 6, 8, 9}, idn]]; Select[ Range[ 0, 90000], cncdQ] (* Harvey P. Dale, Jan 06 2022 *)
PROG
(Python)
import sys
f = open('b274765.txt', 'w')
i = 1
n = 0
a = [""]
while True:
for x in a:
for y in a:
f.write(str(i)+" "+x+"0"+y+"\n")
i += 1
if i>20000:
f.close()
sys.exit()
a = sum([[x+"6", x+"8", x+"9"] for x in a], [])
# Kenny Lau, Jul 05 2016
(PARI) is_a001633(n) = #Str(n)%2==1
is_a001743(n) = #setintersect([1, 2, 3, 4, 5, 7], Set(digits(n)))==0
is_a134808(n) = if(n==0, return(1), if(n < 10, return(0), my(d=digits(n), x=1, y=#d); while(x < #d, if(d[x]==0, break); x++); while(y > 1, if(d[y]==0, break); y--); if(x==y && x==ceil(#Str(n)/2), return(1), return(0))))
is(n) = is_a001633(n) && is_a001743(n) && is_a134808(n) \\ Felix Fröhlich, Jul 05 2016
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Kenny Lau, Jul 05 2016
STATUS
approved