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

1,3

Comments

Every term is congruent to 0 or 1 modulo 9.

Links

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

Formula

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

Example

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

Prog

(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

Crossrefs

Cf. A104113 (squared).

Sequence in context: A119209 A329636 A289520 * A344132 A154389 A041172

Adjacent sequences: A038203 A038204 A038205 * A038207 A038208 A038209

Keyword

nonn,base

Author

Erich Friedman

Extensions

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

Status

approved