A227801 Numbers n whose sum of digits, sum of square of digits and sum of cube of digits all have the same digital root.

1, 9, 10, 11, 19, 36, 47, 63, 74, 90, 91, 99, 100, 101, 109, 110, 111, 119, 136, 147, 163, 174, 190, 191, 199, 306, 316, 333, 360, 361, 369, 396, 407, 417, 444, 470, 471, 479, 497, 603, 613, 630, 631, 639, 666, 693, 704, 714, 740, 741, 749, 777, 794, 900, 901, 909, 910, 911, 919, 936, 947, 963, 974, 990, 991, 999, 1000, 1001

Offset

1,2

Links

Table of n, a(n) for n=1..68.

Example

a(6)=36 since (first power) 3+6=9; (second power) 3^2+6^2=9+36=45 and 4+5=9; (third power) 3^3+6^3=27+216=243 and 2+4+3=9.

Prog

(PARI) dr(n) = if (n, (n-1)%9+1); \\ from A010888
dsq(n) = if (n, d = digits(n); sum(id = 1, #d, d[id]^2));
dcb(n) = if (n, d = digits(n); sum(id = 1, #d, d[id]^3));
ok(n) = (dr(n) == dr(dcb(n))) && (dr(n) == dr(dsq(n))); \\ Michel Marcus, Sep 24 2013

Crossrefs

Cf. A010888 (digital root of n), A007953, A003132, A055012.

Sequence in context: A342147 A045522 A054967 * A048031 A048013 A048048

Adjacent sequences: A227798 A227799 A227800 * A227802 A227803 A227804

Keyword

nonn,base

Author

Carmine Suriano, Sep 23 2013

Extensions

Title improved by Peter Bala, Sep 25 2013

Status

approved