A096257 The least k whose n-th root contains k as a string of digits to the immediate right of the decimal point (excluding leading zeros).

8, 2, 3, 633, 19703, 89, 69, 56, 46, 39, 33, 29, 25, 22, 20, 18, 16, 14, 13, 12, 11, 10, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 138, 133, 128, 124, 120, 116, 113, 109, 106, 103, 100, 97, 95, 92, 90, 87, 85, 83, 81, 79, 77, 75, 74, 72, 70, 69, 67, 66, 65, 63, 62, 61, 59, 58, 57

Offset

2,1

Links

Table of n, a(n) for n=2..72.

Mathematica

f[k_, n_] := Block[{l = Floor[ Log[10, k] + 1], rd = RealDigits[ k^(1/n), 10, 24], id = IntegerDigits[k]}, rdd = Drop[ rd[[1]], rd[[2]]]; While[ rdd[[1]] == 0, rdd = Drop[rdd, 1]]; Take[rdd, l] == id]; g[n_] := Block[{k = 2}, While[IntegerQ[k^(1/n)] || f[k, n] == False, k++ ]; k]; Table[ g[n], {n, 2, 72}]

Prog

(Python)
import re
from sympy import perfect_power
from decimal import *
getcontext().prec = 24
def lzs(s): return len(s) - 2 - len(s[2:].lstrip('0')) # # of leading zeros
def cond(sk, sroot, k, n): # is condition true, with precision verification
    if perfect_power(k, [n]): return False # decimal part should be all 0's
    assert lzs(sroot) + len(sk) < len(sroot) - 3, (n, "increase precision")
    return re.match("0.0*"+sk, sroot)
def a(n):
    k, power = 1, Decimal(1)/Decimal(n)
    rootk, sk = Decimal(k)**power, str(k)
    while not cond(sk, str(rootk - int(rootk)), k, n):
        k += 1
        rootk, sk = Decimal(k)**power, str(k)
    return k
print([a(n) for n in range(2, 73)]) # Michael S. Branicky, Aug 02 2021

Crossrefs

Cf. A074841, A074762.

Sequence in context: A248304 A248303 A298571 * A333206 A357465 A125578

Adjacent sequences: A096254 A096255 A096256 * A096258 A096259 A096260

Keyword

base,nonn

Author

Paul Lusch and Robert G. Wilson v, Jul 31 2004

Status

approved