A068855 a(1) = 1; a(n) is the smallest triangular number > a(n-1) which differs from it at every digit.

1, 3, 6, 10, 21, 36, 45, 66, 78, 91, 105, 210, 325, 406, 528, 630, 703, 820, 903, 1035, 2211, 3003, 4186, 5050, 6105, 7021, 8256, 9045, 10153, 21321, 30135, 41041, 50403, 61075, 70500, 82215, 90100, 101025, 210276, 303031, 411778, 500500, 611065

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..2500

Example

325 belongs to this sequence and the next few triangular numbers are 351, 378, 406, 435; 406 is the smallest one which differs from 325 in all corresponding digit positions.

Prog

(Python)
from math import isqrt
from itertools import count, islice
def alldiff(s, t):
    return all(s[-i]!=t[-i] for i in range(1, min(len(s), len(t))+1))
def diffgreater(n): # smallest number >n that differs from it in every digit
    s = str(n)
    f = str(int(s[0]) + 1)
    return int(f + "".join(("0" if di != "0" else "1") for di in s[1:]))
def agen(): # generator of terms
    an = 1
    while True:
        yield an
        t, s = isqrt(2*diffgreater(an)), str(an)
        while (tt:=t*(t+1)//2)<an or not alldiff(s, str(tt)): t += 1
        an = tt
print(list(islice(agen(), 45))) # Michael S. Branicky, Mar 20 2024

Crossrefs

Cf. A000217, A068853, A068854, A068865.

Sequence in context: A068865 A060179 A056411 * A068882 A076713 A299017

Adjacent sequences: A068852 A068853 A068854 * A068856 A068857 A068858

Keyword

base,nonn

Author

Amarnath Murthy, Mar 12 2002

Extensions

Corrected and extended by Sascha Kurz, Feb 02 2003

Status

approved