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A357075
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Numbers sandwiched between numbers with exactly three distinct prime factors.
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0
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131, 139, 155, 169, 181, 221, 229, 239, 259, 265, 281, 307, 309, 311, 341, 349, 365, 371, 373, 379, 407, 409, 439, 441, 443, 469, 475, 491, 493, 505, 517, 519, 521, 529, 531, 533, 551, 559, 573, 581, 589, 599, 601, 611, 617, 619, 637, 643, 645, 664, 671, 679, 681, 683
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OFFSET
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1,1
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COMMENTS
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Number k such that both k-1 and k+1 are in A033992.
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LINKS
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EXAMPLE
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131 is sandwiched between 130 = 2*5*13 and 132 = 2^2*3*11. Both 130 and 132 have exactly three prime factors. Thus, 131 is in this sequence.
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MATHEMATICA
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Select[Range[1000], Length[FactorInteger[# + 1]] == 3 && Length[FactorInteger[# - 1]] == 3 &]
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PROG
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(Python)
from sympy import factorint
def isA033992(n): return len(factorint(n)) == 3
def ok(n): return isA033992(n-1) and isA033992(n+1)
(PARI) list(lim)=my(v=List(), a=3, b, c); forfactored(n=132, lim\1+1, c=#n[2]~; if(c==3 && a==3, listput(v, n[1]-1)); a=b; b=c); Vec(v) \\ Charles R Greathouse IV, Sep 28 2022
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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