A260193 Numbers k of the form abs(a - b + c - d) such that k^4 equals the concatenation of a//b//c//d and numbers k,b,c,d have the same number of digits.

198, 220, 221, 287, 352, 364, 484, 562, 627, 638, 672, 715, 716, 780, 793, 858, 901, 1095, 1233, 2328, 8905, 18183, 39753, 60248, 85207, 336734, 2727274, 5893504, 8620777, 17769557, 52818678, 70710735, 76470590, 82230444, 101318734, 101636206, 104263158, 105262158, 109891110, 109942690, 117883117, 119722383, 120826541

Offset

1,1

Comments

Leading zeros in b, c, and d are allowed.

Many numbers come in pairs, like: (220, 221), (715, 716), (140017877, 140017878).

Some numbers are also member of A259379, for example: 287, 715, 1095 and also the pair (140017877, 140017878).

Links

Pieter Post, Table of n, a(n) for n = 1..239

Example

198^4 = 1536953616 and 198 = abs (1 - 536 + 953 - 616 ).
8905^4 = 6288335365950625 and 8905 = abs (6288 - 3353 + 6595 - 0625 ).

Mathematica

test[n_] := Block[{L=IntegerLength@ n, v}, v = IntegerDigits[ n^4, 10^L]; Length@ v == 4 && Abs@ Total[ {1, -1, 1, -1} v] == n]; Select[Range[10^5], test] (* Giovanni Resta, Aug 12 2015 *)

Prog

(Python)
def modb(n, m):
    kk = 0
    l = 1
    while n > 0:
        na = n % m
        l += 1
        kk += ((-1)**l) * na
        n //= m
    return abs(kk)
for n in range (100, 10**9):
    ll = len(str(n))
    if modb(n**4, 10**ll) == n and n**4 >= 10**(ll*3):
         print (n, end=', ') # corrected by David Radcliffe, May 09 2025

Crossrefs

Cf. A056733, A101311, A118937, A118938, A228381, A257796, A258482, A259379.

Sequence in context: A286853 A025375 A031512 * A025366 A248534 A334403

Adjacent sequences: A260190 A260191 A260192 * A260194 A260195 A260196

Keyword

nonn,base

Author

Pieter Post, Jul 22 2015

Status

approved