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A262275
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Prime numbers with an even number of steps in their prime index chain.
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11
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3, 11, 17, 41, 67, 83, 109, 127, 157, 191, 211, 241, 277, 283, 353, 367, 401, 461, 509, 547, 563, 587, 617, 739, 773, 797, 859, 877, 967, 991, 1031, 1063, 1087, 1171, 1201, 1217, 1409, 1433, 1447, 1471, 1499, 1597, 1621, 1669, 1723, 1741, 1823, 1913, 2027, 2063, 2081, 2099, 2221, 2269, 2341, 2351
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OFFSET
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1,1
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COMMENTS
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Old (incorrect) name was: Primes not appearing in A121543.
Number of terms less than 10^n: 1, 6, 30, 165, 1024, ... .
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LINKS
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FORMULA
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{ p in primes : A078442(p) mod 2 = 0 }.
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EXAMPLE
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11 is a term: 11 -> 5 -> 3 -> 2 -> 1, four (an even number of) steps "->" = pi = A000720.
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MAPLE
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b:= proc(n) option remember;
`if`(isprime(n), 1+b(numtheory[pi](n)), 0)
end:
a:= proc(n) option remember; local p; p:= a(n-1);
do p:= nextprime(p);
if b(p)::even then break fi
od; p
end: a(1):=3:
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MATHEMATICA
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fQ[n_] := If[ !PrimeQ[n] || (PrimeQ[n] && FreeQ[lst, PrimePi[n]]), AppendTo[lst, n]]; k = 2; lst = {1}; While[k < 2401, fQ@ k; k++]; Select[lst, PrimeQ]
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PROG
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(PARI) b(n)={my(k=0); while(isprime(n), k++; n=primepi(n)); k};
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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