A344630 Primes p such that exactly six numbers among all circular permutations of the digits of p are prime.

193939, 199933, 319993, 331999, 391939, 393919, 919393, 933199, 939193, 939391, 993319, 999331, 1313999, 1317727, 1399913, 1731893, 1743737, 1772713, 1893173, 1977779, 2713177, 3139991, 3173189, 3177271, 3189317, 3717437, 4373717, 7174373, 7271317, 7318931

Offset

1,1

Links

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

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) = subst(Pol(n), x, 10)
is(n) = my(r=rot(digits(n)), i=0); while(r!=digits(n), if(ispseudoprime(eva(r)), i++); r=rot(r)); if(ispseudoprime(eva(r)), i++); if(n==1 || n==11, return(0)); if(i==6, 1, 0)
forprime(p=1, 1e3, if(is(p), print1(p, ", ")))

Crossrefs

Cf. A270083. Row 6 of A317716.

Cf. primes where exactly k numbers among all circular permutations of digits are prime: A068654 (k=1), A344626 (k=2), A344627 (k=3), A344628 (k=4), A344629 (k=5), A344631 (k=7), A344632 (k=8).

Sequence in context: A258508 A254995 A232202 * A131907 A202937 A013901

Adjacent sequences: A344627 A344628 A344629 * A344631 A344632 A344633

Keyword

nonn,base

Author

Felix Fröhlich, May 25 2021

Status

approved