A082382 Table which contains in row n the track of n->A003132(n) until reaching 1 or 4.

1, 1, 2, 4, 3, 9, 81, 65, 61, 37, 58, 89, 145, 42, 20, 4, 4, 16, 37, 58, 89, 145, 42, 20, 4, 5, 25, 29, 85, 89, 145, 42, 20, 4, 6, 36, 45, 41, 17, 50, 25, 29, 85, 89, 145, 42, 20, 4, 7, 49, 97, 130, 10, 1, 8, 64, 52, 29, 85, 89, 145, 42, 20, 4, 9, 81, 65, 61, 37, 58, 89, 145, 42, 20

Offset: 1

Author

Cino Hilliard, Apr 13 2003

Keywords

• easy
• nonn
• base
• tabf

Comments

If n=1 or 4, the row is extended until reaching 1 or 4 a second time after the starting value.

Conjecture: Each sequence terminates with 1 or the 4 16 37 58 89 145 42 20 4... loop.

Examples

			The table starts in row 1 as
1,1 ;
2,4 ;
3,9,81,65,61,37,58,89,145,42,20,4;
4,16,37,58,89,145,42,20,4;
5,25,29,85,89,145,42,20,4;
6,36,45,41,17,50,25,29,85,89,145,42,20,4;
		

References

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

Programs

PARI

\ The squared digital root of a number output initial terms digitsq2(m) = {y=0; for(x=1,m, digitsq(x) ) } digitsq(n) = { print1(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

Redefined as an irregular table, merged 8 and 9 to 89 at one place - R. J. Mathar, Mar 14 2010