A038206 Can express a(n) with the digits of a(n)^2 in order, only adding plus signs.

0, 1, 9, 10, 36, 45, 55, 82, 91, 99, 100, 235, 297, 369, 370, 379, 414, 657, 675, 703, 756, 792, 909, 918, 945, 964, 990, 991, 999, 1000, 1296, 1702, 1782, 2223, 2728, 3366, 3646, 3682, 4132, 4879, 4906, 4950, 5050, 5149, 5292, 6832, 7191, 7272, 7389

Offset: 1

Author

Erich Friedman

Keywords

• nonn
• base

Comments

Every term is congruent to 0 or 1 modulo 9.

Examples

			82^2 = 6724 and 6+72+4 = 82.
		

Links

• Max Alekseyev and Giovanni Resta, Table of n, a(n) for n = 1..3200 (first 408 terms from Max Alekseyev)

Crossrefs

Cf. A104113 (squared).

Programs

Python

def expr(t, d): # can you express target t with digits d, only adding +'s
    if t < 0: return False
    if t == int(d): return True
    return any(expr(t-int(d[:i]), d[i:]) for i in range(1, len(d)))
def ok(n): return expr(n, str(n*n))
print(list(filter(ok, range(7500)))) # Michael S. Branicky, Sep 27 2021

Formula

a(n) = sqrt(A104113(n)). - Andrea Tarantini, Sep 27 2021

Extensions

Offset corrected and b-file added by Max Alekseyev, Jun 08 2018