A358847 a(n) = 1 if A053669(6*n) [the smallest prime not dividing 6*n] is of the form 6m-1, otherwise a(n) = 0.

1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions.

Formula

a(n) = A358755(6*n).

a(n) = A358846(n-1) XOR A358846(n), where XOR is bitwise-XOR, A003987. See comments in A358755.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 6 * Sum_{p prime, p == 5 (mod 6)} ((p-1)/(Product_{q prime, q <= p} q)) = 0.8261626908... . - Amiram Eldar, Apr 16 2024

Example

For n = 85085 = 5*7*11*13*17, 6*n = A002110(7) = 510510, whose smallest nondividing prime is 19, which is of the form 6m+1, therefore a(85085) = 0.
For n = 1616615 = 5*7*11*13*17*19, 6*n = A002110(8), whose smallest nondividing prime is 23, which is of the form 6m-1, therefore a(1616615) = 1.
For n = 37182145 = 5*7*11*13*17*19*23, 6*n = A002110(9), whose smallest nondividing prime is 29, which is of the form 6m-1, therefore a(37182145) = 1. This is the first case where the alternating pattern following A276084 breaks.

Prog

(PARI)
A053669(n) = forprime(p=2, , if(n%p, return(p)));
A358847(n) = (5 == (A053669(6*n)%6));
(PARI) a(n)=forprime(p=5, , if(n%p, return(p%6==5))) \\ Charles R Greathouse IV, Dec 03 2022, corrected by Antti Karttunen, Apr 14 2024

Crossrefs

Characteristic function of A358849, whose complement A358848 gives the positions of zeros.

Cf. A002110, A003987, A276084, A358755, A358846.

Cf. also asymptotics of A353528 and A353529.

Sequence in context: A099443 A132342 A156174 * A187967 A106467 A106468

Adjacent sequences: A358844 A358845 A358846 * A358848 A358849 A358850

Keyword

nonn,easy

Author

Antti Karttunen, Dec 03 2022

Status

approved