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A353528
a(n) = 1 if A053669(n) [the smallest prime not dividing n] is of the form 4m+1, otherwise a(n) = 0.
10
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0
OFFSET
1
FORMULA
If A353526(n) = 1, then a(n) = 1, otherwise a(n) = 0.
a(n) = A059841(n) - A353529(n).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{p prime, p == 1 (mod 4)} ((p-1)/(Product_{q prime, q <= p} q)) = 0.1337642792... . - Amiram Eldar, Jul 25 2022
MATHEMATICA
f[n_] := Module[{p = 2}, While[Divisible[n, p], p = NextPrime[p]]; p]; a[n_] := If[Mod[f[n], 4] == 1, 1, 0]; Array[a, 100] (* Amiram Eldar, Jul 25 2022 *)
PROG
(PARI)
A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
A353528(n) = (1==(A053669(n)%4));
CROSSREFS
Characteristic function of A353530.
Cf. also A353488.
Not the same as A319691(25+n).
Sequence in context: A025458 A286925 A179527 * A358755 A172051 A093958
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 24 2022
STATUS
approved