A347189 Positive integers that can be expressed as the sum of powers of their digits (from right to left) with consecutive natural exponents.

1, 2, 3, 4, 5, 6, 7, 8, 9, 24, 332, 1676, 121374, 4975929, 134116265, 1086588775, 3492159897, 8652650287, 8652650482

Offset

1,2

Comments

Any number > 9 consisting of just one digit (A014181) can't be in the list. (Provable using the Carmichael function.)

Links

Table of n, a(n) for n=1..19.

Example

24 = 4^2 + 2^3 is a term.
332 = 2^3 + 3^4 + 3^5 is another term.

Prog

(Python)
liste = []
for ex in range(0, 20):
    for t in range(1, 10000):
        n = t
        pot = ex
        ergebnis = 0
        while n > 0:
            pot = pot + 1
            rest = n % 10
            n = (n - rest) // 10
            zw = 1
            for i in range(pot):
                zw = zw * rest
            ergebnis = ergebnis + zw
        if (int(ergebnis) == t) and (t not in liste):
            liste.append(t)
liste.sort()
print(liste)
(Python)
def powsum(digits, startexp):
    return sum(digits[i]**(startexp+i) for i in range(len(digits)))
def ok(n):
    if n < 10: return True
    s = str(n)
    if set(s) <= {'0', '1'}: return False
    digits, startexp = list(map(int, s))[::-1], 1
    while powsum(digits, startexp) < n: startexp += 1
    return n == powsum(digits, startexp)
print(list(filter(ok, range(2*10**5)))) # Michael S. Branicky, Aug 29 2021

Crossrefs

Cf. A023052, A032799, A014181.

Sequence in context: A061862 A007532 A349279 * A068189 A069716 A095289

Adjacent sequences: A347186 A347187 A347188 * A347190 A347191 A347192

Keyword

nonn,base,more

Author

Reiner Moewald, Aug 21 2021

Extensions

a(15)-a(19) from Michael S. Branicky, Aug 31 2021

Status

approved