A344628 Primes p such that exactly four numbers among all circular permutations of the digits of p are prime.

1193, 1931, 3119, 3779, 7793, 7937, 9311, 9377, 11393, 11701, 11717, 11743, 13177, 13931, 13997, 16993, 17011, 17117, 17431, 17539, 17713, 19717, 19997, 21737, 23339, 23773, 30197, 31139, 31699, 31771, 32377, 33923, 37217, 38197, 39233, 39499, 39799, 39971

Offset

1,1

Links

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

Mathematica

Select[Prime[Range[4500]], Count[FromDigits/@Table[RotateRight[IntegerDigits[#], d], {d, IntegerLength[ #]}], _?PrimeQ]==4&] (* Harvey P. Dale, Aug 31 2024 *)

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==4, 1, 0)
forprime(p=1, 1e3, if(is(p), print1(p, ", ")))

Crossrefs

Cf. A270083. Row 4 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), A344629 (k=5), A344630 (k=6), A344631 (k=7), A344632 (k=8).

Sequence in context: A040104 A103171 A032530 * A353263 A287049 A153379

Adjacent sequences: A344625 A344626 A344627 * A344629 A344630 A344631

Keyword

nonn,base

Author

Felix Fröhlich, May 25 2021

Status

approved