A262988 Number of distinct primes, including n if prime, obtained by cyclically shifting the digits of n.

0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 1, 0, 1, 2, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 1, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 2, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0

Offset

1,13

Comments

First differs from A039999 at n = 103.

Differs from A061264 iff n is a term of A004022.

a(n) = A055642(n) iff n is a term of A068652, except when n is also in A004022.

Links

Felix Fröhlich, Table of n, a(n) for n = 1..10000

Example

a(1013) = 2, because of the four cyclic permutations of the digits of 1013 (1013, 131, 1310, 3101) two, namely 1013 and 131, are prime and those two primes are distinct.

Mathematica

f[n_] := Block[{len = IntegerLength@ n, s = {n}}, Do[AppendTo[s, FromDigits@ RotateRight@ IntegerDigits@ s[[k - 1]]], {k, 2, len}]; DeleteDuplicates@ Select[s, PrimeQ]]; Array[ Length@ f@ # &, {87}] (* Michael De Vlieger, Oct 07 2015 *)

Prog

(PARI) rot(n) = if(#Str(n)==1, v=vector(1), v=vector(#n-1)); for(i=2, #n, v[i-1]=n[i]); u=vector(#n); for(i=1, #n, u[i]=n[i]); v=concat(v, u[1]); v
eva(n) = x=0; for(k=1, #n, x=x+(n[k]*10^(#n-k))); x
a(n) = i=0; r=rot(digits(n)); while(r!=digits(n), if(ispseudoprime(eva(r)), i++); r=rot(r)); if(ispseudoprime(eva(r)), i++); i

Crossrefs

Cf. A016114, A039999, A045978, A061264, A068652, A068653, A068654, A069219, A247153.

Sequence in context: A328515 A356682 A323989 * A039999 A069842 A083056

Adjacent sequences: A262985 A262986 A262987 * A262989 A262990 A262991

Keyword

nonn,base

Author

Felix Fröhlich, Oct 06 2015

Status

approved