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A365248
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Composite numbers k that are not a prime minus one, for which A214749(k) = k/2.
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2
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34, 94, 118, 142, 202, 214, 246, 274, 298, 334, 394, 402, 436, 454, 514, 526, 538, 622, 628, 634, 694, 706, 712, 754, 766, 778, 802, 814, 892, 898, 922, 934, 942, 958, 1002, 1006, 1042, 1054, 1114, 1126, 1132, 1138, 1146, 1158, 1174, 1198, 1234, 1246, 1270
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OFFSET
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1,1
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COMMENTS
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As can be seen from A214749, for most composites k that are not a prime minus one, the smallest value of m that satisfies k-m | k^2+m is smaller than k/2. This sequence lists the exceptions.
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LINKS
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PROG
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(Python)
from sympy import isprime
a=[]
for n in range(2, 1000):
for m in range(1, n//2+1):
if (n**2+m)%(n-m)==0:
if m==n/2 and not isprime(n+1):
a.append(n)
break
print(a)
(Python)
from itertools import count, islice
from sympy import isprime
from sympy.abc import x, y
from sympy.solvers.diophantine.diophantine import diop_quadratic
def A365248_gen(startvalue=2): # generator of terms >= startvalue
return filter(lambda n:not isprime(n+1) and min(int(x) for x, y in diop_quadratic(n*(n-y)+x*(y+1)) if x>0)==n>>1, count(max(startvalue+startvalue&1, 2), 2))
(PARI) f(n) = my(m=1); while((n^2+m) % (n-m), m++); m; \\ A214749
lista(nn) = my(list=List()); forcomposite(c=1, nn, if ((f(c) == c/2) && !isprime(c+1), listput(list, c))); Vec(list); \\ Michel Marcus, Sep 08 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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