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

1,2

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)

References

C. Stanley Ogilvy, Tomorrow's Math, 1972

Links

Table of n, a(n) for n=1..72.

Example

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)

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; ) }

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: A361067 A359654 A061104 * A155931 A309801 A248245

Adjacent sequences: A082378 A082379 A082380 * A082382 A082383 A082384

Keyword

nonn,base,easy,tabf

Author

Cino Hilliard, Apr 13 2003

Extensions

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

Status

approved