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A262275
Prime numbers with an even number of steps in their prime index chain.
11
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
OFFSET
1,1
COMMENTS
Old (incorrect) name was: Primes not appearing in A121543.
Number of terms less than 10^n: 1, 6, 30, 165, 1024, ... .
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1025 terms from Zak Seidov and Robert G. Wilson v)
Michael P. May, Properties of Higher-Order Prime Number Sequences, Missouri J. Math. Sci. (2020) Vol. 32, No. 2, 158-170; and arXiv version, arXiv:2108.04662 [math.NT], 2021.
FORMULA
From Alois P. Heinz, Mar 15 2020: (Start)
{ p in primes : A078442(p) mod 2 = 0 }.
a(n) = prime(A333242(n)). (End)
EXAMPLE
11 is a term: 11 -> 5 -> 3 -> 2 -> 1, four (an even number of) steps "->" = pi = A000720.
MAPLE
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:
seq(a(n), n=1..60); # Alois P. Heinz, Mar 15 2020
MATHEMATICA
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]
PROG
(PARI) b(n)={my(k=0); while(isprime(n), k++; n=primepi(n)); k};
apply(prime, select(n->b(n)%2, [1..500])) \\ Michel Marcus, Jan 03 2022; after A333242
CROSSREFS
Cf. A000040, A000720, A078442, A121543, A333242 (complement in primes).
Sequence in context: A240084 A100567 A270225 * A176804 A078116 A245045
KEYWORD
nonn
AUTHOR
EXTENSIONS
New name from Alois P. Heinz, Mar 15 2020
STATUS
approved