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A377313
Numbers that are not hexateron (5-simplex) numbers.
1
2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71
OFFSET
1,1
COMMENTS
Complement of A000389. Numbers k such that 120*k is not a product of 5 consecutive integers.
FORMULA
a(n) = n+m if n+m>binomial(m+4,5), a(n) = n+m-2 if n+m-2<binomial(m+3,5) and a(n) = n+m-1 otherwise where m = floor((120n)^(1/5)).
PROG
(Python)
from math import comb
from sympy import integer_nthroot
def A377313(n): return n+(m:=integer_nthroot(120*n, 5)[0])+(0 if n>(k:=comb(m+4, 5)-m) else -2 if n-2<k-comb(m+3, 4) else -1)
CROSSREFS
Cf. A000389.
Sequence in context: A080907 A127161 A129657 * A249407 A360305 A103679
KEYWORD
nonn,easy
AUTHOR
Chai Wah Wu, Oct 24 2024
STATUS
approved