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A082381
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Sequence of the squared digital root of a number until 1 or 4 is reached. The initial numbers 1,2,..n are not output.
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1
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1, 4, 9, 81, 65, 61, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 25, 29, 85, 89, 145, 42, 20, 4, 36, 45, 41, 17, 50, 25, 29, 85, 89, 145, 42, 20, 4, 49, 97, 130, 10, 1, 64, 52, 29, 85, 89, 145, 42, 20, 4, 81, 65, 61, 37, 58, 89, 145, 42, 20, 4, 1, 2, 4, 5, 25, 29
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Conjecture: The sequence always terminates with 1 or the 4 16 37 58 89 145 42 20 4... loop (cf. A080709).
(Contribution from M. F. Hasler, Dec 18 2009, Start)
This sequence should be read as fuzzy table, where the n-th row contains the successive results under the map "sum of digits squared", when starting with n, until either 1 or 4 is reached. So either of these two marks the end of a row: See example.
Row lengths (i.e. "stopping times") are given in A171250. (End)
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REFERENCES
| C. Stanley Ogilvy, Tomorrow's Math, 1972
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EXAMPLE
| (Contribution from M. F. Hasler, Dec 18 2009, Start) The table reads:
[n=1] 1 (n=1 -> 1^2=1 -> STOP)
[n=2] 4 (n=2 -> 2^2=4 -> STOP)
[n=3] 9,81,65,61,37,58,89,145,42,20,4 (n=3 -> 3^2=9 -> 9^2=81 -> 8^2+1^2=65 -> ...)
[n=4] 16,37,58,89,145,42,20,4 (n=4 -> 4^2=16 -> 1^2+6^2=37 -> 3^2+7^2=58 -> ...)
...
[n=7] 49,97,130,10,1 (n=7 -> 7^2=49 -> 4^2+9^2=97 -> 130 -> 10 -> 1 -> STOP)
etc. (End)
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PROG
| (PARI) digitsq2(m) = {y=0; for(x=1, m, digitsq(x) ) }
/* The squared digital root of a number */ digitsq(n) = { while(1, s=0; while(n > 0, d=n%10; s = s+d*d; n=floor(n/10); ); print1(s" "); if(s==1 || s==4, break); n=s; ) }
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CROSSREFS
| Cf. A082382 (list also the initial value); sequences ending in the 4-loop: A000216 (n=2), A000218 (n=3), A080709 (n=4), A000221 (n=5), A008460 (n=6), A008462 (n=8), A008462 (n=9), A139566 (n=15), A122065 (n=74169); sequences ending in 1: A000012 (n=1), A008461 (n=7). [From M. F. Hasler, Dec 18 2009]
Sequence in context: A041597 A041030 A061104 * A155931 A077530 A115551
Adjacent sequences: A082378 A082379 A082380 * A082382 A082383 A082384
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KEYWORD
| nonn,base,easy
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Apr 13 2003
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EXTENSIONS
| Corrected and edited, added explanations M. F. Hasler (www.univ-ag.fr/~mhasler), Dec 18 2009
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