A162393 Fibonacci numbers equal to a promic number or an anagram of a promic number.

2, 21, 6765, 10946, 2178309, 14930352, 102334155, 701408733, 1134903170, 4807526976, 20365011074, 32951280099, 225851433717, 1548008755920, 10610209857723, 72723460248141, 117669030460994, 498454011879264, 2111485077978050, 3416454622906707

Offset

1,1

Comments

There are many terms overlapping with A162394. 13 of the first 20 terms are in A162394. - Chai Wah Wu, Dec 26 2016

Links

Michael S. Branicky, Table of n, a(n) for n = 1..28

Example

a(1) = A000045(3) = 2 is the promic number A002378(1).
a(2) = A000045(8) = 21 is an anagram of 12 = A002378(3).
a(3) = A000045(20) = 6765 is an anagram of 7656= A002378(87).
a(4) = A000045(21) = 10946 is an anagram of 19460 = A002378(139) and 96410 = A002378(310).
a(5) = A000045(32) = 2178309 is an anagram of 7308912 = A002378(2703), of 8017392 = A002378(2831) and of 9731280 = A002378(3119).

Maple

Digits := 200 ; digFreq := proc(n) dgs := convert(n, base, 10) ; c := [seq(0, j=0..9)] ; for d in dgs do c := subsop(d+1= op(d+1, c)+1, c) ; od: c; end:
isAna := proc(a, b) RETURN( digFreq(a) = digFreq(b)) ; end:
isA002378 := proc(n) k := floor(sqrt(n)) ; RETURN(k*(k+1) = n ) ; end:
A055642 := proc(n) max(1, ilog10(n)+1) ; end:
for n from 1 do f := combinat[fibonacci](n) ; fdgs := A055642(f) ; for k from floor(sqrt(10^(fdgs-1))) do p := k*(k+1) ; if A055642(p) > fdgs then break; fi; if isAna(p, f) then printf("%d, \n", f) ; break; fi; od; od: # R. J. Mathar, Aug 14 2009

Prog

(Python)
from math import isqrt
from itertools import count, islice
def promics(d): # generator of promic numbers with d digits
    ilb, lb, ub = isqrt(10**(d-1)-1), 10**(d-1), 10**d
    if d == 1: yield 0
    for i in count(ilb):
        p = i*(i+1)
        if p < lb: continue
        elif p >= ub: break
        yield p
def agen(): # generator of sequence terms
    # yield 0  # uncomment if 0 is inserted
    f, g, n, adict = 1, 2, 1, dict()
    for d in count(1):
        P = set("".join(sorted(str(p))) for p in promics(d))
        while f < 10**d:
            if "".join(sorted(str(f))) in P: yield f
            f, g = g, f+g
print(list(islice(agen(), 16))) # Michael S. Branicky, Feb 19 2024

Crossrefs

Cf. A000045, A002378, A162394.

Sequence in context: A195165 A201973 A278737 * A328993 A336768 A180700

Adjacent sequences: A162390 A162391 A162392 * A162394 A162395 A162396

Keyword

nonn,base

Author

Claudio Meller, Jul 02 2009

Extensions

Six more terms from R. J. Mathar, Aug 14 2009

a(13)-a(18) from Donovan Johnson, Oct 11 2009

a(19)-a(20) from Chai Wah Wu, Jan 02 2017

Status

approved