A162394 Fibonacci numbers (A000045) which are anagrams of Triangular numbers (A000217).

0, 1, 3, 21, 55, 2584, 28657, 2178309, 5702887, 14930352, 102334155, 267914296, 701408733, 2971215073, 4807526976, 7778742049, 12586269025, 32951280099, 225851433717, 591286729879, 1548008755920, 10610209857723, 27777890035288, 72723460248141, 308061521170129, 498454011879264, 806515533049393, 1304969544928657, 3416454622906707

Offset

1,3

Links

Michael S. Branicky, Table of n, a(n) for n = 1..38 (all terms <= 20 digits)

Example

2584 is A000045(18) and is an anagram of 2485 = A000217(70).
28567 is A000045(23) and is an anagram of 67528 = A000217(367).

Prog

(Python)
from math import isqrt
from itertools import count, islice
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
    yield 0
    f, g, n, adict = 1, 2, 1, dict()
    for d in count(1):
        T = set("".join(sorted(str(t))) for t in tris(d))
        while f < 10**d:
            if "".join(sorted(str(f))) in T: yield f
            f, g = g, f+g
print(list(islice(agen(), 20))) # Michael S. Branicky, Feb 18 2024

Crossrefs

Cf. A000045, A000217.

Sequence in context: A033567 A181156 A356809 * A129212 A354850 A328042

Adjacent sequences: A162391 A162392 A162393 * A162395 A162396 A162397

Keyword

nonn,base

Author

Claudio Meller, Jul 02 2009

Extensions

Edited and extended by Ray Chandler, Jul 09 2009

a(24)-a(29) from Chai Wah Wu, Dec 25 2016

Status

approved