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 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
 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; text; internal format)
 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). (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) REFERENCES C. Stanley Ogilvy, Tomorrow's Math, 1972 LINKS 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) 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: A041597 A041030 A061104 * A155931 A248245 A077530 Adjacent sequences:  A082378 A082379 A082380 * A082382 A082383 A082384 KEYWORD nonn,base,easy AUTHOR Cino Hilliard, Apr 13 2003 EXTENSIONS Corrected and edited, added explanations M. F. Hasler, Dec 18 2009 STATUS approved

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