A166596 - OEIS

%I #13 Feb 18 2024 13:28:40

%S 0,120,4095,36046,147153,219453,1021735,1053426,104653,10149765,

%T 10294453,10348975,100486576,10725396,103428153,20759346,12347965,

%U 100174935,129548656,102968425,104697685,102925378,160249753,123865930,126047503,102538360,224073865

%N Smallest triangular number with exactly n anagrams that are triangular numbers.

%H Michael S. Branicky, <a href="/A166596/b166596.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..46 from Chai Wah Wu)

%e n=1, {0} (triangular number with no nontrivial anagram)

%e n=2, {120,210} (two anagrams of triangular numbers)

%e n=3, {4095,4950,9045} (three anagrams of triangular numbers)

%e n=4, {36046,43660,46360,66430} (four anagrams of triangular numbers)

%e n=5, {147153,375411,435711,713415,741153}

%e n=6, {219453,243951,432915,493521,539241,943251}

%e n=7, {1021735,1710325,2310175,2375110,3201715,5312170,7321051}

%e n=8, {1053426,1345620,1360425,1405326,1624503,2465310,5643120,6503421}

%e n=9, {104653,135460,354061,403651,406351,431056,465130,534061,634501}

%e n=10, {10149765,14609715,15149760,16974051,17461095,17609145,41509716,41591760, 41756091,61710495}.

%o (Python)

%o from math import isqrt

%o from collections import Counter

%o from itertools import count, islice, combinations_with_replacement as mc

%o def tris(d): # generator of triangular numbers with d digits

%o     ilb, lb, ub = isqrt(2*10**(d-1))-1, 10**(d-1), 10**d

%o     if d == 1: yield 0

%o     for i in count(ilb):

%o         t = i*(i+1)//2

%o         if t < lb: continue

%o         elif t >= ub: break

%o         yield t

%o def agen(): # generator of sequence terms

%o     n, adict = 1, dict()

%o     for d in count(1):

%o         c = Counter("".join(sorted(str(t))) for t in tris(d))

%o         for t in tris(d):

%o             v = c["".join(sorted(str(t)))]

%o             if v not in adict: adict[v] = t

%o             while n in adict: yield adict[n]; n += 1

%o print(list(islice(agen(), 46))) # _Michael S. Branicky_, Feb 18 2024

%Y Cf. A034291 Triangular numbers that have some nontrivial permutation of digits which is also triangular.

%K base,nonn

%O 1,2

%A _Zak Seidov_, Oct 17 2009