A082381 Sequence of the squared digital root of a number until 1 or 4 is reached. The initial numbers 1,2,..n are not output.

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

Offset: 1

Author

Cino Hilliard, Apr 13 2003

Keywords

• nonn
• base
• easy
• tabf

Comments

Conjecture: The sequence always terminates with 1 or the 4 16 37 58 89 145 42 20 4... loop (cf. A080709).

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)

Examples

			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)
		

References

• C. Stanley Ogilvy, Tomorrow's Math, 1972

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]

Programs

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; ) }

Extensions

Corrected and edited, added explanations M. F. Hasler, Dec 18 2009