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A371900
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Numbers k such that k+1 is composite and A371641(k) != p^2 where p = A020639(k+1) is the smallest prime factor of k+1.
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2
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406, 766, 988, 1036, 1072, 1138, 1246, 1396, 1402, 1456, 1500, 1642, 1738, 1762, 1768, 1816, 1918, 1926, 1942, 2076, 2116, 2158, 2182, 2278, 2506, 2716, 2746, 2812, 2866, 2920, 2992, 3076, 3148, 3172, 3286, 3316, 3382, 3496, 3568, 3682, 3706, 3712, 3742, 3762
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OFFSET
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1,1
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COMMENTS
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If k+1 is composite, then A371641(k) <= A020639(k+1)^2. This sequence lists numbers k where the inequality is strict.
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LINKS
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PROG
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(Python)
from itertools import count, islice
from sympy import isprime, primefactors, factorint, integer_log
def A371900_gen(startvalue=2): # generator of terms >= startvalue
for n in count(max(startvalue, 2)):
if not isprime(n+1):
q = min(primefactors(n+1))
for m in range(4, q**2):
f = factorint(m)
if sum(f.values()) > 1:
c = 0
for p in sorted(f):
a = pow(n, integer_log(p, n)[0]+1, m)
for _ in range(f[p]):
c = (c*a+p)%m
if not c:
yield n
break
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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