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%I #22 Mar 20 2024 11:48:51
%S 1,3,6,10,21,36,45,66,78,91,105,210,325,406,528,630,703,820,903,1035,
%T 2211,3003,4186,5050,6105,7021,8256,9045,10153,21321,30135,41041,
%U 50403,61075,70500,82215,90100,101025,210276,303031,411778,500500,611065
%N a(1) = 1; a(n) is the smallest triangular number > a(n-1) which differs from it at every digit.
%H Michael S. Branicky, <a href="/A068855/b068855.txt">Table of n, a(n) for n = 1..2500</a>
%e 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.
%o (Python)
%o from math import isqrt
%o from itertools import count, islice
%o def alldiff(s, t):
%o return all(s[-i]!=t[-i] for i in range(1, min(len(s), len(t))+1))
%o def diffgreater(n): # smallest number >n that differs from it in every digit
%o s = str(n)
%o f = str(int(s[0]) + 1)
%o return int(f + "".join(("0" if di != "0" else "1") for di in s[1:]))
%o def agen(): # generator of terms
%o an = 1
%o while True:
%o yield an
%o t, s = isqrt(2*diffgreater(an)), str(an)
%o while (tt:=t*(t+1)//2)<an or not alldiff(s, str(tt)): t += 1
%o an = tt
%o print(list(islice(agen(), 45))) # _Michael S. Branicky_, Mar 20 2024
%Y Cf. A000217, A068853, A068854, A068865.
%K base,nonn
%O 1,2
%A _Amarnath Murthy_, Mar 12 2002
%E Corrected and extended by _Sascha Kurz_, Feb 02 2003
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