A257763
Zeroless numbers n such that n and n^2 have the same set of decimal digits.
Original entry on oeis.org
1, 4762, 4832, 12385, 14829, 26394, 34196, 36215, 49827, 68474, 72576, 74528, 79286, 79836, 94583, 94867, 96123, 98376, 123385, 123546, 124235, 124365, 124579, 124589, 125476, 125478, 126969, 129685, 135438, 139256, 139261, 139756, 149382, 152385, 156242
Offset: 1
4762 is in the sequence because it is zeroless and 4762^2 = 22676644 has the same set of decimal digits as 4762: {2,4,6,7}.
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a:= proc(n) option remember; local k, s;
for k from 1+`if`(n=1, 0, a(n-1)) do
s:= {convert(k, base, 10)[]};
if not 0 in s and s={convert(k^2, base, 10)[]}
then return k fi
od
end:
seq(a(n), n=1..10);
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sameQ[n_]:=Union[IntegerDigits[n]]==Union[IntegerDigits[n^2]];Select[Range@156242,And[FreeQ[IntegerDigits[#],0],sameQ[#]]&] (* Ivan N. Ianakiev, May 08 2015 *)
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isok(n) = vecmin(d=digits(n)) && Set(d) == Set(digits(n^2)); \\ Michel Marcus, May 31 2015
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A257763_list = [n for n in range(1,10**6) if not '0' in str(n) and set(str(n)) == set(str(n**2))] # Chai Wah Wu, May 31 2015
A257774
Numbers n such that the products of the decimal digits of n^2 and n^3 coincide, n^2 and n^3 are zeroless.
Original entry on oeis.org
1, 5, 7, 6057, 292839, 1295314, 4897814, 4967471, 5097886, 6010324, 6919146, 7068165, 7189558, 9465077, 15347958, 22842108, 24463917, 26754863, 43378366, 48810128, 48885128, 50833026, 54588458, 54649688, 68093171, 69925865, 69980346, 73390374, 74357144
Offset: 1
5 is in the sequence since 5^2 = 25 and 5^3 = 125 and we have 2*5 = 1*2*5 = 10 > 0.
6057 is in the sequence since 6057^2 = 36687249 and 6057^3 = 222214667193 and we have 3*6*6*8*7*2*4*9 = 2*2*2*2*1*4*6*6*7*1*9*3 = 435456 > 0.
A257968
Zeroless numbers n such that the product of digits of n, the product of digits of n^2 and the product of digits of n^3 form a geometric progression.
Original entry on oeis.org
1, 2, 38296, 151373, 398293, 422558, 733381, 971973, 2797318, 3833215, 6988327, 7271256, 8174876, 8732657, 9872323, 9981181, 11617988, 11798921, 14791421, 15376465, 15487926, 15625186, 16549885, 18543639, 21316582, 21492828, 22346329, 22867986, 23373644
Offset: 1
38296 is in the sequence because the pod equals 2592 (=3*8*2*9*6), pod(38296^2) is 622080, pod(38296^3) is 149299200. 2592*240 = 622080 => 622080*240 = 149299200.
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pod[n_]:=Times@@IntegerDigits@n; Select[Range[10^8], pod[#^3] pod[#] == pod[#^2]^2 >0 &] (* Vincenzo Librandi, May 16 2015 *)
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pod(n) = my(d = digits(n)); prod(k=1, #d, d[k]);
isok(n) = (pd = pod(n)) && (pdd = pod(n^2)) && (pdd/pd == pod(n^3)/pdd); \\ Michel Marcus, May 30 2015
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def pod(n):
kk = 1
while n > 0:
kk= kk*(n%10)
n =int(n//10)
return kk
for i in range (1,10**7):
if pod(i**3)*pod(i)==pod(i**2)**2 and pod(i**2)!=0:
print (i, pod(i),pod(i**2),pod(i**3),pod(i**2)//pod(i))
Showing 1-3 of 3 results.
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