A023052 -id:A023052 - cp's OEIS frontend

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

Reiner Moewald, Aug 21 2021

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

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

Cf. A023052, A032799, A014181.

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)

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

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

A333670 Numbers m such that m equals abs(d_1^k - d_2^k + d_3^k - d_4^k ...), where d_i is the decimal expansion of m and k is some power greater than 2.

Original entry on oeis.org

0, 1, 48, 240, 407, 5920, 5921, 2918379, 7444416, 18125436, 210897052, 6303187514, 8948360198, 10462450356, 11647261846, 18107015789, 27434621679, 31332052290, 4986706842391, 485927682264092, 1287253463537089, 126835771455251081, 559018292730428520, 559018292730428521

Offset: 1

Pieter Post, Apr 01 2020

For terms > 1, the exponents k are 2, 4, 3, 4, 4, 7, 8, 8, 11, 11, 21, 11, 11, 11, 11, 13, 15, 16, 22, 21, 21.

			48 = abs(4^2 - 8^2), 5920 = abs(5^4 - 9^4 + 2^4 - 0^4).

Cf. A005188, A007770, A023052.

def moda(n,a):
    kk,j = 0,1
    while n > 0:
        kk= kk-j*(n%10)**a
        n,j =int(n//10),-j
    return abs(kk)
for i in range (0,10**7):
    for t in range(2,21):
        if i==moda(i,t):
            print (i)
            break

a(19)-a(24) from Giovanni Resta, Apr 02 2020

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Python

Python

Extensions

A333670 Numbers m such that m equals abs(d_1^k - d_2^k + d_3^k - d_4^k ...), where d_i is the decimal expansion of m and k is some power greater than 2.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Python

Extensions