A275804 Numbers with at most one nonzero digit on each digit slope of the factorial base representation of n.

0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 16, 18, 20, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 36, 37, 40, 42, 44, 48, 49, 50, 51, 52, 60, 61, 64, 66, 68, 72, 73, 76, 78, 79, 82, 90, 96, 98, 102, 104, 108, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 132, 133, 136, 138, 140, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 156, 157, 160

Offset: 0

Author

Antti Karttunen, Aug 10 2016

Keywords

• nonn
• base

Comments

Indexing starts from zero, because a(0) = 0 is a special case in this sequence.

Numbers n for which A275947(n) = 0 or equally, for which A275811(n) <= 1.

Numbers n for which A008683(A275734(n)) <> 0, that is, indices of squarefree terms in A275734.

Numbers n for which A060130(n) = A060502(n).

Numbers with at most one nonzero digit on each digit slope of the factorial base representation of n (see A275811 and A060502 for the definition of slopes in this context). More exactly: numbers n in whose factorial base representation (A007623) there does not exist a pair of digit positions i_1 and i_2 with nonzero digits d_1 and d_2, such that (i_1 - d_1) = (i_2 - d_2).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to factorial base representation

Crossrefs

Complement: A275805.

Indices of zeros in A275947 and A275962.

Intersection with A276005 gives A261220.

Cf. A059590 (a subsequence).

Cf. A007623, A008683, A060130, A060502, A275734, A275811.

Programs

Python

from operator import mul
from sympy import prime, factorial as f
from sympy.ntheory.factor_ import core
def a007623(n, p=2): return n if n
0 else '0' for i in x)[::-1]
    return 0 if n==1 else sum([int(y[i])*f(i + 1) for i in range(len(y))])
def a(n): return 1 if n==0 else a275732(n)*a(a257684(n))
def ok(n): return 1 if n==0 else core(a(n))==a(n)
print([n for n in range(201) if ok(n)]) # Indranil Ghosh, Jun 19 2017