A359012 Numbers k that are a substring of xPy where k=concatenation(x,y) and xPy is the number of permutations A008279(x,y).

318, 557, 692, 729, 2226, 2437, 2776, 3209, 4436, 5336, 5549, 5718, 5956, 6068, 6141, 6353, 6958, 7045, 7046, 7338, 7345, 7643, 7865, 8261, 8409, 9153, 9178, 9242, 9544, 9569, 9664, 9894, 9999, 10174, 10889, 12389, 12434, 13497, 13516, 16308, 18695, 19707, 21940, 21954, 22535

Offset

1,1

Comments

If n and d are two nonnegative integers, and d <= n, then the number of permutations is obtained by the formula nPd = n!/(n-d)!.

Links

Table of n, a(n) for n=1..45.

Example

318 is present in 31P8 (= 318073392000 = A008279(31, 8)).
557 is present in 55P7 (= 1022755734000 = A008279(55, 7)).
692 is present in 69P2 (= 4692 = A008279(69, 2)).

Prog

(Python)
import math
def is_valid_sequence_number(n):
    num_str = str(n)
    length = len(num_str)
    for count in range(math.ceil(length / 2), length):
        if num_str in str(
            math.perm(int(num_str[:count]), int(num_str[-(length - count) :]))
        ):
            return True
    return False
A359012 = []
for num in range(10, 10**4):
    if is_valid_sequence_number(num):
        A359012.append(num)
(PARI) T(n, k) = n!/(n-k)!; \\ A008279
isok(k) = my(d=digits(k), s=Str(k), d1, d2); for (i=1, #d-1, d1=fromdigits(Vec(d, i)); d2=fromdigits(vector(#d-i, k, d[i+k])); if ((d1 >= d2) && (#strsplit(Str(T(d1, d2)), s) > 1), return(1)); ); \\ Michel Marcus, Dec 12 2022

Crossrefs

Cf. A008279.

Sequence in context: A323327 A323328 A045272 * A278131 A075153 A204835

Adjacent sequences: A359009 A359010 A359011 * A359013 A359014 A359015

Keyword

nonn,base

Author

John Samuel, Dec 11 2022

Status

approved