A001742 -id:A001742 - cp's OEIS frontend

A034905 Numbers whose square contains no loops in its digits (assumes 1, 2, 3, 5, 7 have no loops and 0, 4, 6, 8, 9 do).

1, 5, 11, 15, 35, 39, 61, 85, 111, 115, 165, 189, 235, 239, 335, 365, 389, 415, 461, 485, 611, 715, 1061, 1085, 1165, 1235, 1239, 1489, 1585, 1665, 1765, 1885, 2261, 2285, 2715, 3335, 3365, 3489, 3511, 3515, 3635, 3711, 3915, 3939, 3965, 4139, 4211, 4715

Offset: 1

J. Lowell

			13^2 = 169 contains a 6 and a 9, so 13 does not belong to the sequence.

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A031153, A001742.

Select[Range[5000],ContainsAll[{1,2,3,5,7},IntegerDigits[#^2]]&] (* Giorgos Kalogeropoulos, Jul 30 2021 *)

A190223 Numbers all of whose divisors are numbers whose decimal digits are noncomposite numbers (1,2,3,5,7).

Original entry on oeis.org

1, 2, 3, 5, 7, 11, 13, 15, 17, 21, 22, 23, 25, 31, 33, 35, 37, 51, 53, 55, 71, 73, 75, 77, 111, 113, 115, 121, 125, 127, 131, 137, 151, 155, 157, 173, 175, 211, 213, 217, 221, 223, 227, 231, 233, 251, 253, 257, 271, 275, 277, 311, 313, 317, 331, 337, 353

Offset: 1

Jaroslav Krizek, May 06 2011

Subset of A001742.

All terms are obviously odd except for 2 and numbers of the form 2*A004022(k). - Harvey P. Dale, May 28 2014 (corrected by Iain Fox, Sep 03 2020)

			Number 115 is in sequence because all divisors of 115 (1, 5, 23, 115) are numbers whose decimal digits are noncomposite numbers (1,2,3,5,7).

Iain Fox, Table of n, a(n) for n = 1..10000 (first 1000 terms from G. C. Greubel)

Supersequence: A001742.

Cf. A004022, A243534.

ncnQ[n_]:=Module[{digs=Union[Flatten[IntegerDigits/@Divisors[n]]]}, Complement[ digs,{1,2,3,5,7}]=={}]; Select[ Range[ 400],ncnQ] (* Harvey P. Dale, May 28 2014 *)

is(k) = fordiv(k, d, if(setminus(vecsort(digits(d), , 8), [1, 2, 3, 5, 7]) != [], return(0))); 1 \\ Iain Fox, Dec 28 2017

More terms from Harvey P. Dale, May 28 2014

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

Original entry on oeis.org

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

A113623 7-smooth numbers containing only noncomposite digits (1,2,3,5,7).

Original entry on oeis.org

1, 2, 3, 5, 7, 12, 15, 21, 25, 27, 32, 35, 72, 75, 112, 125, 135, 175, 225, 252, 315, 375, 512, 525, 735, 1125, 1152, 1215, 1225, 1323, 1372, 1512, 1575, 1715, 2352, 3125, 3375, 13122, 13125, 15552, 25515, 25725, 31752, 35721, 55125, 77175, 111132

Offset: 1

Amarnath Murthy, Nov 10 2005

			175 is a term since 175 = 5^2*7 and contains digits 1,5,7 none of which is composite. 175 is a member of A002473.

Intersection of A001742 and A002473.

Cf. A113624.

isA002473 := proc(n) local ifs ; if n <= 10 then true ; else ifs := ifactors(n)[2] ; if max( seq(op(1,i),i=ifs) ) <= 7 then true; else false ; fi ; fi ; end: isA113623 := proc(n) local digs ; if isA002473(n) then if convert(convert(n,base,10),set) minus {1,2,3,5,7} <> {} then false ; else true ; fi ; else false ; fi ; end: for n from 1 to 150000 do if isA113623(n) then printf("%d, ",n) ; fi ; od; # R. J. Mathar, Aug 28 2007

More terms from R. J. Mathar, Aug 28 2007

Name corrected by Andrew Howroyd, Sep 17 2024

A136975 Numbers k such that k and k^2 use only the digits 1, 2, 3, 5 and 7.

Original entry on oeis.org

1, 5, 11, 15, 35, 111, 115, 235, 335, 715, 1235, 2715, 3335, 3511, 3515, 3711, 12335, 27115, 33335, 33515, 35711, 37115, 72335, 75711, 111235, 123335, 132335, 177515, 333335, 333515, 357115, 572115, 575515, 577515, 723335, 757115, 1233335, 1312335, 1323335, 3333335, 3333515, 3512511, 5227115, 5772115, 7233335, 11212115, 11277115, 11735515

Offset: 1

Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008

Generated with DrScheme.
Sequence is infinite; e.g., it contains 3...35 = (10^n-1)/3 + 2 for all n. - Robert Israel, Nov 24 2015
a(n) mod 100 can be only 11, 15 or 35 for n > 2. So if a(n) is a prime number, a(n) mod 100 = 11 for n > 2. Initial prime values of a(n) are 11, 3511 and 12375511 for n > 2. - Altug Alkan, Nov 25 2015

			757313127132715^2 = 573523172527531752317223271225.

Jonathan Wellons, Table of n, a(n) for n = 1..330
J. Wellons, Tables of Shared Digits [archived]

Cf. A001742, A034905.

f2:= proc(n) local L; convert(convert(n^2,base,10),set) intersect {4,6,8,9,0} = {} end proc:
S:= {0}: A:= {}:
for d from 1 to 8 do
  S:={seq(seq(10*s+j,j=[1,2,3,5,7]),s=S)};
  A:= select(f2,S) union A;
od:
sort(convert(A,list)); # Robert Israel, Nov 24 2015, corrected Sep 03 2020

w = {1, 2, 3, 5, 7}; Select[Range[1, 10^7, 2], Union[IntegerDigits@ #, IntegerDigits[#^2], w] == w &] (* Michael De Vlieger, Nov 25 2015 *)

cp's OEIS Frontend

A034905 Numbers whose square contains no loops in its digits (assumes 1, 2, 3, 5, 7 have no loops and 0, 4, 6, 8, 9 do).

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A190223 Numbers all of whose divisors are numbers whose decimal digits are noncomposite numbers (1,2,3,5,7).

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

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A113623 7-smooth numbers containing only noncomposite digits (1,2,3,5,7).

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A136975 Numbers k such that k and k^2 use only the digits 1, 2, 3, 5 and 7.

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Mathematica