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A179464
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a(n) = min(nextprime(n),nextsemiprime(n)).
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1
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2, 3, 4, 5, 6, 7, 9, 9, 10, 11, 13, 13, 14, 15, 17, 17, 19, 19, 21, 21, 22, 23, 25, 25, 26, 29, 29, 29, 31, 31, 33, 33, 34, 35, 37, 37, 38, 39, 41, 41, 43, 43, 46, 46, 46, 47, 49, 49, 51, 51, 53, 53, 55, 55, 57, 57, 58, 59, 61, 61, 62, 65, 65, 65, 67, 67, 69, 69, 71, 71, 73, 73, 74, 77, 77, 77, 79, 79, 82, 82, 82, 83, 85, 85, 86, 87, 89, 89, 91, 91, 93, 93, 94
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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n=1: nextprime(1)=2, nextsemiprime(1)=4, hence a(1)=2,
n=2: nextprime(2)=3, nextsemiprime(2)=4, hence a(2)=3,
n=3: nextprime(3)=5, nextsemiprime(3)=4, hence a(3)=4.
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MAPLE
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PS:= select(t -> numtheory:-bigomega(t)<=2, [$2..500]):
Res:= NULL:
k:= 1;
for n from 2 to max(PS) do
if n > PS[k] then k:= k+1 fi;
Res:= Res, PS[k];
od:
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MATHEMATICA
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Table[m=n+1; While[2!= Plus@@Last/@FactorInteger[m], m++]; Min[NextPrime[n], m], {n, 200}]
mnp[n_]:=Module[{s=n+1}, While[PrimeOmega[s]!=2, s++]; Min[NextPrime[n], s]]; Array[mnp, 100] (* Harvey P. Dale, Apr 23 2019 *)
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PROG
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(PARI) {for(n=1, 200, m=n+1; while(2<>bigomega(m), m++); print(min(nextprime(n+1), m)))}
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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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