A251755 Digital root of n + n^2.

0, 2, 6, 3, 2, 3, 6, 2, 9, 9, 2, 6, 3, 2, 3, 6, 2, 9, 9, 2, 6, 3, 2, 3, 6, 2, 9, 9, 2, 6, 3, 2, 3, 6, 2, 9, 9, 2, 6, 3, 2, 3, 6, 2, 9, 9, 2, 6, 3, 2, 3, 6, 2, 9, 9, 2, 6, 3, 2, 3, 6, 2, 9, 9, 2, 6, 3, 2, 3, 6, 2, 9, 9, 2, 6, 3, 2, 3, 6, 2, 9, 9, 2, 6, 3, 2, 3, 6, 2, 9, 9, 2, 6, 3, 2, 3, 6, 2, 9, 9, 2, 6, 3, 2, 3

Offset: 0

Author

Peter M. Chema, Dec 07 2014

Keywords

• nonn
• base
• easy

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.

a(n) equals the digital root sum of A010888 and A056992.

Examples

			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.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 1).

Crossrefs

Cf. A002378, A010888, A056992.

Programs

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 *)

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

Formula

a(n) = A010888(A002378(n)).