A327822 Numbers k such that when cyclically permuting the digits of k any number of times, any prime obtained is followed by a composite number and vice-versa.

14, 16, 19, 20, 23, 29, 30, 32, 34, 35, 38, 41, 43, 47, 50, 53, 59, 61, 67, 70, 74, 76, 83, 89, 91, 92, 95, 98, 1015, 1018, 1070, 1075, 1099, 1132, 1136, 1163, 1216, 1238, 1274, 1303, 1321, 1339, 1361, 1475, 1510, 1517, 1535, 1570, 1574, 1612, 1630, 1631, 1636

Offset

1,1

Links

Table of n, a(n) for n=1..53.

Example

When cyclically permuting the digits of 961990 one gets the numbers 961990, 619909, 199096, 990961, 909619, 96199 and these numbers are composite, prime, composite, prime, composite, prime, respectively, so 961990 (and each of these cyclic permutations except 96199) is a term of the sequence.
A more graphical representation:
       961990              C
      /      \           /   \
  096199   619909       P     P
     |        |         |     |
  909619   199096       C     C
      \      /           \   /
       990961              P

Prog

(PARI) eva(n) = subst(Pol(n), x, 10)
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
is(n) = my(nn=#Str(n), u=[], v=vector(nn, x, x%2==0), w=vector(nn, x, x%2==1), d=digits(n), r=rot(d)); if(nn%2==1, return(0)); u=concat(u, [ispseudoprime(eva(d))]); u=concat(u, ispseudoprime(eva(r))); while(1, r=rot(r); if(r==d, if(u==v || u==w, return(1)); return(0)); u=concat(u, ispseudoprime(eva(r))))

Crossrefs

Cf. A068652, A068654, A270083.

Sequence in context: A034305 A091898 A061365 * A102107 A217707 A176686

Adjacent sequences: A327819 A327820 A327821 * A327823 A327824 A327825

Keyword

nonn,base

Author

Felix Fröhlich, Sep 26 2019

Status

approved