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
Examples
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)).
Crossrefs
Cf. A008279.
Programs
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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
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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)
Comments