A064210 -id:A064210 - cp's OEIS frontend

A122484 Numbers k not ending in zero such that the sum of digits of k is >= the sum of digits of k^4 (in base 10).

1, 7, 19, 67, 124499, 594959999, 1349969999, 57999659949, 84936699999, 498998999999

Offset: 1

Martin Raab, Sep 15 2006

I've also found 498998999999, 7494994999999, 34999974999999 and some larger numbers, but not all values in between have been checked.
One is likely to find an example of the form 5*10^j - m*10^floor(j/2) - 1 or 7.5*10^j - m*10^floor(j/2) - 1 for j > 12 within the first 10^(floor(j/2)-1) m's.
Is this sequence finite? - Charles R Greathouse IV, Jan 12 2012
This sequence is infinite: for N = 7.5*10^j - 40*10^floor(j/2) - 1 one has A007953(N) = 9j-2 and A007953(N^4) <= 9j-2 for all j > 16, with equality for all even j > 16. - M. F. Hasler, Jan 14 2012
a(11) > 10^12. - Delbert L. Johnson, May 01 2023

			67 is a term because 67 has a digital sum of 13 and 67^4 = 20151121 which also has a digital sum of 13.
594959999 has a digital sum of 68 and 594959999^4 has a digital sum of 67, i.e., less than 68.

Cf. A064210.

is_A122484(n)= n%10 && A007953(n) >= A007953(n^4) \\ M. F. Hasler, Jan 14 2012

A122484 = { k in A067251 | A007953(k) >= A007953(k^4) }. - M. F. Hasler, Jan 14 2012

a(8) and a(9) from Martin Raab, Oct 17 2008

a(10) from Delbert L. Johnson, May 01 2023

A204324 Numbers k such that A007953(k) >= A007953(k^3), where A007953 = digital sum in base 10.

Original entry on oeis.org

0, 1, 8, 10, 80, 100, 171, 378, 468, 487, 577, 585, 586, 587, 684, 800, 1000, 1710, 3780, 4680, 4870, 4877, 5770, 5850, 5851, 5860, 5868, 5870, 6840, 8000, 10000, 15877, 17100, 28845, 28847, 28885, 28887, 37800, 46800, 46877, 48700, 48770, 48784, 49468

Offset: 1

M. F. Hasler, Jan 14 2012

When k is in the sequence, then 10*k is in the sequence, too.

Cf. A064399, A064209, A064210.

Select[Range[0,51000],Total[IntegerDigits[#]]>=Total[IntegerDigits[#^3]]&] (* Harvey P. Dale, Jul 05 2025 *)

for(n=0,1e6, A007953(n)>=A007953(n^3)&print1(n","))

A204324 = A064209 union A070276.

A261439 Sum of the digits of n exceeds the sum of the digits of n^4.

Original entry on oeis.org

124499, 1244990, 12449900, 124499000, 594959999, 1244990000, 1349969999, 5949599990, 12449900000, 13499699990, 59495999900

Offset: 1

Jeppe Stig Nielsen, Aug 18 2015

A comment by M. F. Hasler in A122484 shows that there are infinitely many terms not divisible by 10.

A122484 is the main sequence.

Cf. A064209, A064399, A064210, A007953.

is(n)=sumdigits(n)>sumdigits(n^4) \\ Charles R Greathouse IV, Aug 18 2015

from itertools import count, islice
def A261439_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n: sum(int(d) for d in str(n)) > sum(int(d) for d in str(n**4)), count(max(startvalue,1)))
A261439_list = list(islice(A261439_gen(),3)) # Chai Wah Wu, Oct 20 2023

cp's OEIS Frontend

A122484 Numbers k not ending in zero such that the sum of digits of k is >= the sum of digits of k^4 (in base 10).

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A204324 Numbers k such that A007953(k) >= A007953(k^3), where A007953 = digital sum in base 10.

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A261439 Sum of the digits of n exceeds the sum of the digits of n^4.

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