A001743 -id:A001743 - cp's OEIS frontend

A274765 Cyclops numbers with circular digits {0,6,8,9}.

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

Kenny Lau, Jul 05 2016

Intersection of A001743 and A134808.

			86069 is a member because it is cyclops (A134808) and each digit contains at least one loop (A001743).

Kenny Lau, Table of n, a(n) for n = 1..20000

Cf. A001633, A001742, A134808, A160561.

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 *)

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

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

A261449 Prime numbers whose decimal digits contain a total of two loops.

Original entry on oeis.org

83, 109, 149, 181, 199, 269, 281, 283, 349, 383, 401, 419, 439, 443, 461, 463, 467, 479, 491, 509, 569, 587, 599, 601, 607, 619, 641, 643, 647, 659, 661, 691, 709, 769, 787, 811, 821, 823, 827, 853, 857, 877, 907, 919, 929, 941, 947, 967, 991, 997, 1019, 1039

Offset: 1

Altug Alkan, Aug 19 2015

Of the digits, 0 through 9, {0, 4, 6, 9} have one loop, 8 has two loops, and all the rest have none. - Robert G. Wilson v, Aug 20 2015

			83 is the first term of the sequence. The digit 8 contains two closed curves.

Cf. A001729, A190222, A001743, A001744, A001745, A249572.

Select[Prime@ Range@ 200, 2 == Total[{ 1,0, 0,0, 1,0, 1,0, 2,1}[[1 + IntegerDigits@ #]]]&] (* Giovanni Resta, Aug 19 2015 *)

More terms from Giovanni Resta, Aug 19 2015

A329542 a(n) is the first occurrence of a composite number whose factorization without exponents contains exactly n circular loops (i.e., loops in digits 0, 6, 8, 9) on each side of the equals sign.

Original entry on oeis.org

76, 166, 801, 8067, 38804, 88181, 586668, 3680818, 6899086, 40888802, 168888169, 868862887, 884888909, 4088888618, 6898889086, 40888888618, 108088888891, 864888888892, 1928888888668, 16888888880873, 8848888888909, 40888888888802, 120888888888896, 968888888886830

Offset: 1

G. L. Honaker, Jr., Nov 16 2019

			a(1) = 76 because 76 = 2*2*19, and there is exactly one loop on each side of the equals sign.
a(2) = 166 because 166 = 2*83, and there are exactly two loops on each side of the equals sign, etc. Note that '8' contains two loops.

Chris K. Caldwell and G. L. Honaker, Jr., Prime Curios! 76

Cf. A000040, A001743.

cntLo[n_] := Plus @@ ({1,0,0,0,0,0,1,0,2,1}[[IntegerDigits[n] + 1]]);  cntF[n_] := Plus @@ (cntLo /@ First /@ FactorInteger[n]); a[n_] := Block[{k=1}, While[ cntLo[k] != n || cntF[k] != n || PrimeQ[k], k++]; k]; Array[a, 8] (* Giovanni Resta, Nov 18 2019 *)

a(5)-a(10) from Chuck Gaydos

a(11)-a(24) from Giovanni Resta, Nov 18 2019

cp's OEIS Frontend

A274765 Cyclops numbers with circular digits {0,6,8,9}.

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A261449 Prime numbers whose decimal digits contain a total of two loops.

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A329542 a(n) is the first occurrence of a composite number whose factorization without exponents contains exactly n circular loops (i.e., loops in digits 0, 6, 8, 9) on each side of the equals sign.

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