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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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,changed

AUTHOR

Pieter Post, May 07 2015

EXTENSIONS

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

STATUS

approved

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Last modified October 3 16:31 EDT 2022. Contains 357237 sequences. (Running on oeis4.)