A068834 Squares k such that k and the next three squares also have a square digit sum.

81, 100, 121, 144, 400, 10000, 10201, 10404, 12100, 40000, 1000000, 1002001, 1004004, 1020100, 1172889, 1210000, 1232100, 2604996, 4000000, 4297329, 4485924, 6185169, 11048976, 11108889, 12916836, 14584761, 16353936, 23040000

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Formula

{k^2 | k, k+1, k+2 and k+3 in A061910}. = Michael S. Branicky, Feb 11 2026

Example

81 is a term since the sum of the digits of 81, 100, 121 and 144 are 9, 1, 4 and 9, all square.

Prog

(Python)
from math import isqrt
from itertools import count, islice
def c(k): return isqrt(r:=sum(map(int, str(k))))**2 == r
def agen(): # generator of terms
    c1, c2, c3, c4 = list(map(c, [1, 4, 9, 16]))
    for k in count(5):
        if all([c1, c2, c3, c4]): yield (k-4)**2
        c1, c2, c3, c4 = c2, c3, c4, c(k*k)
print(list(islice(agen(), 32))) # Michael S. Branicky, Feb 11 2026

Crossrefs

Cf. A061910, A068833.

Sequence in context: A381821 A335066 A179444 * A067521 A117686 A104113

Adjacent sequences: A068831 A068832 A068833 * A068835 A068836 A068837

Keyword

nonn,base

Author

Amarnath Murthy, Mar 09 2002

Extensions

More terms from Sascha Kurz, Mar 26 2002

Name clarified and a(29) onward from Michael S. Branicky, Feb 11 2026

Status

approved