A344627 - OEIS

A344627

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

113, 131, 197, 199, 311, 337, 373, 719, 733, 919, 971, 991, 1031, 1091, 1097, 1103, 1109, 1123, 1181, 1213, 1231, 1279, 1297, 1301, 1319, 1327, 1579, 1777, 1811, 1873, 1913, 1949, 1951, 1979, 1987, 1993, 2131, 2311, 2377, 2399, 2713, 2791, 2939, 2971, 3011

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OFFSET

1,1

LINKS

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

MATHEMATICA

Select[Prime[Range[500]], Total[Boole[PrimeQ[FromDigits/@ Table[ RotateRight[ IntegerDigits[#], n], {n, IntegerLength[#]}]]]]==3&] (* Harvey P. Dale, Mar 30 2023 *)

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==3, 1, 0)

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

CROSSREFS

Cf. A270083. Row 3 of A317716.

Cf. primes where exactly k numbers among all circular permutations of digits are prime: A068654 (k=1), A344626 (k=2), A344628 (k=4), A344629 (k=5), A344630 (k=6), A344631 (k=7), A344632 (k=8).

Sequence in context: A163760 A179911 A376213 * A187867 A216288 A224554

Adjacent sequences: A344624 A344625 A344626 * A344628 A344629 A344630

KEYWORD

nonn,base

AUTHOR

Felix Fröhlich, May 25 2021

STATUS

approved