A068854 a(1) = 1; a(n) is the smallest square > a(n-1) which differs from it at every digit.

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 225, 361, 400, 529, 676, 729, 841, 900, 1024, 2116, 3025, 4356, 5041, 6400, 7056, 8100, 9025, 10201, 21025, 30276, 42025, 50176, 61009, 70225, 81796, 90000, 101124, 210681, 302500, 410881, 501264, 613089, 702244, 810000

Offset

1,2

Links

David A. Corneth, Table of n, a(n) for n = 1..2200

David A. Corneth, PARI program

Example

225 is a term and the next few squares are 256, 289, 324, 361, 400, 441, ...; 361 is the smallest one which differs from 225 in all corresponding digit positions.

Prog

(PARI) \\ See PARI link
(Python)
from math import isqrt
from itertools import count, islice
def alldiff(s, t):
    return all(s[-i]!=t[-i] for i in range(1, min(len(s), len(t))+1))
def diffgreater(n): # smallest number >n that differs from it in every digit
    s = str(n)
    f = str(int(s[0]) + 1)
    return int(f + "".join(("0" if di != "0" else "1") for di in s[1:]))
def agen(): # generator of terms
    an = 1
    while True:
        yield an
        r, s = isqrt(diffgreater(an)), str(an)
        while not alldiff(s, str(r*r)): r += 1
        an = r*r
print(list(islice(agen(), 45))) # Michael S. Branicky, Mar 20 2024

Crossrefs

Cf. A000290, A068853.

Sequence in context: A179334 A068867 A068864 * A111704 A052041 A018884

Adjacent sequences: A068851 A068852 A068853 * A068855 A068856 A068857

Keyword

base,nonn

Author

Amarnath Murthy, Mar 12 2002

Extensions

Name corrected by Jon E. Schoenfield, Oct 27 2023

a(9) onward corrected by Sean A. Irvine, Mar 18 2024

Status

approved