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A001273 Smallest number that takes n steps to reach 1 under iteration of sum-of-squares-of-digits map (= smallest "happy number" of height n). 6
1, 10, 13, 23, 19, 7, 356, 78999 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Subsequent terms are too large to display in full.

a(8) = 3789 * 10^973 - 1 (3788 followed by 973 9's).

a(9) = 78889 * 10^((a(8) - 305)/81) - 1 (78888 followed by (421 * 10^973 - 34)/9 9's, specified by Warut Roonguthai for UPINT3).

a(10) = 259 * 10^((a(9) - 93)/81) - 1.

a(11) = 179 * 10^((a(10) - 114)/81) - 1.

a(12) = 47 * 10^((a(11) - 52)/81) - 1.

REFERENCES

Richard K. Guy, Unsolved Problems in Number Theory, Sect. E34. (2nd ed. UPINT2 = 1994, 3rd ed. UPINT3 = 2004)

LINKS

Table of n, a(n) for n=0..7.

Tianxin Cai & Xia Zhou, On The Heights of Happy Numbers, Rocky Mountain J. Math., Vol. 38, No. 6 (2008), 1921-1926.

H. G. Grundman, E. A. Teeple, Heights of happy numbers and cubic happy numbers, Fib Quart. 41 (4) (2003) 301

Hans Havermann, Big and Happy

May Mei, Andrew Read-McFarland, Numbers and the Heights of their Happiness, arXiv:1511.01441 [math.NT], 2015.

CROSSREFS

Cf. A007770, A018785, A176762.

Sequence in context: A191969 A018785 A176762 * A111524 A074346 A126973

Adjacent sequences:  A001270 A001271 A001272 * A001274 A001275 A001276

KEYWORD

base,nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

a(7), a(8) from Jud McCranie, Sep 15 1994

a(9)-a(12) from Hans Havermann, May 02 2010

Edited by Hans Havermann, May 03 2010, May 04 2010

STATUS

approved

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Last modified August 18 23:54 EDT 2017. Contains 290782 sequences.