OFFSET
0,2
COMMENTS
Positive integers give a cycle of period 9: {2, 6, 3, 2, 3, 6, 2, 9, 9}, which may be expressed as a decimal expansion of 87745433/333333333. Note that a(-n)=a(n-1), and negative integers give a mirrored period cycle, generating the cycle in reverse. Sequence is palindromic.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 1).
EXAMPLE
For a(7) = 2 because 7+7^2 = 56, and 5+6 = 11, yielding result of digital root of 2 (1+1).
For a(-3) = 6 because -3+(-3)^2 = -6, with digital root of 6.
MATHEMATICA
a251755[n_Integer] := Module[{f},
f[x_] := Last@NestWhileList[Plus @@ IntegerDigits[#] &, x, # > 9 &];
f /@ Table[i + i^2, {i, 0, n}]]; a251755[60] (* Michael De Vlieger, Dec 17 2014 *)
PROG
(PARI) DR(n)=s=sumdigits(n); while(s>9, s=sumdigits(s)); s
for(n=0, 100, print1(DR(abs(n+n^2)), ", ")) \\ Derek Orr, Dec 30 2014
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Peter M. Chema, Dec 07 2014
STATUS
approved