A166596 Smallest triangular number with exactly n anagrams that are triangular numbers.

0, 120, 4095, 36046, 147153, 219453, 1021735, 1053426, 104653, 10149765, 10294453, 10348975, 100486576, 10725396, 103428153, 20759346, 12347965, 100174935, 129548656, 102968425, 104697685, 102925378, 160249753, 123865930, 126047503, 102538360, 224073865

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..46 from Chai Wah Wu)

Example

n=1, {0} (triangular number with no nontrivial anagram)
n=2, {120,210} (two anagrams of triangular numbers)
n=3, {4095,4950,9045} (three anagrams of triangular numbers)
n=4, {36046,43660,46360,66430} (four anagrams of triangular numbers)
n=5, {147153,375411,435711,713415,741153}
n=6, {219453,243951,432915,493521,539241,943251}
n=7, {1021735,1710325,2310175,2375110,3201715,5312170,7321051}
n=8, {1053426,1345620,1360425,1405326,1624503,2465310,5643120,6503421}
n=9, {104653,135460,354061,403651,406351,431056,465130,534061,634501}
n=10, {10149765,14609715,15149760,16974051,17461095,17609145,41509716,41591760, 41756091,61710495}.

Prog

(Python)
from math import isqrt
from collections import Counter
from itertools import count, islice, combinations_with_replacement as mc
def tris(d): # generator of triangular numbers with d digits
    ilb, lb, ub = isqrt(2*10**(d-1))-1, 10**(d-1), 10**d
    if d == 1: yield 0
    for i in count(ilb):
        t = i*(i+1)//2
        if t < lb: continue
        elif t >= ub: break
        yield t
def agen(): # generator of sequence terms
    n, adict = 1, dict()
    for d in count(1):
        c = Counter("".join(sorted(str(t))) for t in tris(d))
        for t in tris(d):
            v = c["".join(sorted(str(t)))]
            if v not in adict: adict[v] = t
            while n in adict: yield adict[n]; n += 1
print(list(islice(agen(), 46))) # Michael S. Branicky, Feb 18 2024

Crossrefs

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

Sequence in context: A231136 A222003 A139389 * A000514 A179060 A342073

Adjacent sequences: A166593 A166594 A166595 * A166597 A166598 A166599

Keyword

base,nonn

Author

Zak Seidov, Oct 17 2009

Status

approved