A257768 Numbers m such that for some power k, m is the sum of d + d^k as d runs through the digits of m.

12, 18, 30, 90, 666, 870, 960, 1998, 7816, 42648, 119394, 302034, 360522, 1741752, 12051036, 909341082, 931186956, 1136424308, 1145082306, 8390370196, 49388550660, 52927388760, 100552730520, 41845367362266, 51671446297908, 245917854035004, 607628544623816, 858683110606660, 4023730658941192

Offset

1,1

Comments

The power k of most terms in this sequence is equal to or one more or one less than the number of digits in the term. One exception is 302034: 302034 = 3^9 + 0^9 + 2^9 + 0^9 + 3^9 + 4^9 + 3+0+2+0+3+4.

Links

Table of n, a(n) for n=1..29.

Example

666 = (6+6+6) + (6^3 + 6^3 + 6^3).
7816 = (7+8+1+6) + (7^4 + 8^4 + 1^4 + 6^4).
360522 = (3+6+0+5+2+2) + (3^7 + 6^7 + 0^7 + 5^7 + 2^7 + 2^7).

Maple

mmax:= 10:  # to get all terms < 10^mmax
Res:= NULL:
score:= (c, p) -> add(c[i+1]*(i+i^p), i=0..9):
for m from 2 to mmax do
comps:= convert(map(`-`, combinat:-composition(10+m, 10), [1$10]), list):
for c in comps do
  cL:= [seq(i$c[i+1], i=0..9)];
  if max(c[3..-1]) = 0 then slim:= 0 else slim:= 10^m fi;
  for p from 1 do
    s:= score(c, p);
    L:= sort(convert(s, base, 10));
    if L = cL then Res:= Res, s; break fi;
    if s >= slim then break fi;
  od:
od:
od:
sort([Res]); # Robert Israel, May 08 2015

Prog

(Python)
# WARNING: this prints numbers in the sequence, but not in increasing order.
def moda(n, a):
    kk = 0
    while n > 0:
        kk= kk+(n%10)**a
        n = n//10
    return kk
def sod(n):
    kk = 0
    while n > 0:
        kk += n % 10
        n = n//10
    return kk
for a in range (1, 10):
    for c in range (10, 10**6):
        if c == moda(c, a)+sod(c):
            print(c, end=", ")

Crossrefs

Cf. A115518, A130680, A111434.

Sequence in context: A075281 A171179 A333869 * A007371 A277725 A319746

Adjacent sequences: A257765 A257766 A257767 * A257769 A257770 A257771

Keyword

base,nonn

Author

Pieter Post, May 07 2015

Extensions

a(14)-a(29) from Giovanni Resta, May 08 2015

Status

approved