A080472 a(n) = smallest triangular number that is obtained by placing digits anywhere in n; a(n) = n if n is a triangular number.

1, 21, 3, 45, 15, 6, 78, 28, 91, 10, 171, 120, 136, 1431, 15, 136, 171, 1081, 190, 120, 21, 1225, 231, 2145, 253, 276, 276, 28, 2926, 300, 231, 325, 3003, 2346, 325, 36, 378, 378, 3916, 406, 741, 4278, 435, 4465, 45, 406, 4278, 1485, 496, 1540, 351, 528, 153, 1540

Offset: 1

Author

Amarnath Murthy, Mar 07 2003

Keywords

• base
• nonn

Links

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

Crossrefs

Cf. A068164, A068165, A080470, A080471.

Programs

Python

from math import isqrt
from itertools import count
def dmo(n, t):
    if t < n: return False
    while n and t:
        if n%10 == t%10:
            n //= 10
        t //= 10
    return n == 0
def a(n):
    return next(t for t in (i*(i+1)//2 for i in count(isqrt(2*n))) if dmo(n, t))
print([a(n) for n in range(1, 77)]) # Michael S. Branicky, Jan 21 2023

Extensions

More terms from Ray Chandler, Oct 11 2003