A090293 Least k > n such that the decimal expansion of k^2 ends in n^2.

10, 9, 8, 7, 46, 15, 44, 43, 42, 41, 90, 239, 488, 237, 486, 35, 484, 233, 482, 231, 80, 229, 478, 227, 476, 75, 474, 223, 472, 221, 70, 219, 2468, 1217, 2466, 285, 2464, 1213, 2462, 1289, 460, 1209, 2458, 1293, 2456, 205, 2454, 1297, 2452, 1201, 150, 1301

Offset

0,1

Links

Michael S. Branicky, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe)

Formula

a(n) = A090292(n)^(1/2).

Mathematica

Table[k = n; d = IntegerDigits[n^2]; len = Length[d]; While[k++; Take[IntegerDigits[k^2], -len] != d]; k, {n, 0, 51}] (* T. D. Noe, Mar 23 2012 *)

Prog

(Python)
def a(n):
    k, target = n + 1, str(n*n)
    while not str(k*k).endswith(target): k += 1
    return k
print([a(n) for n in range(52)]) # Michael S. Branicky, Oct 09 2021
(Python) # alternate version
from math import isqrt
def issquare(n): return isqrt(n)**2 == n
def a(n):
    k, target = 1, str(n*n)
    while not issquare(int(str(k)+target)): k += 1
    return isqrt(int(str(k)+target))
print([a(n) for n in range(52)]) # Michael S. Branicky, Oct 09 2021

Crossrefs

Cf. A090292.

Sequence in context: A055121 A249591 A132674 * A164732 A070562 A216557

Adjacent sequences: A090290 A090291 A090292 * A090294 A090295 A090296

Keyword

base,nonn

Author

Amarnath Murthy, Nov 29 2003

Extensions

More terms from Vladeta Jovovic, Jun 18 2004

Status

approved