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

Author

Martin Raab, Sep 15 2006

Keywords

• base
• nonn
• more

Comments

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

Examples

			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.
		

Crossrefs

Cf. A064210.

Programs

PARI

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

Formula

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

Extensions

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

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