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A344626 Primes p such that exactly two numbers among all circular permutations of the digits of p are prime. 7
13, 17, 31, 37, 71, 73, 79, 97, 101, 103, 107, 127, 149, 157, 163, 173, 181, 191, 271, 277, 307, 313, 317, 331, 359, 367, 379, 397, 419, 479, 491, 571, 577, 593, 617, 631, 673, 701, 709, 727, 739, 757, 761, 787, 797, 811, 839, 877, 907, 911, 937, 941, 947, 977 (list; graph; refs; listen; history; text; internal format)
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==2, 1, 0)

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

CROSSREFS

Cf. A270083. Row 2 of A317716.

Cf. primes where exactly k numbers among all circular permutations of digits are prime: A068654 (k=1), A344627 (k=3), A344628 (k=4), A344629 (k=5), A344630 (k=6), A344631 (k=7), A344632 (k=8).

Sequence in context: A180526 A161401 A225035 * A006567 A263240 A246043

Adjacent sequences:  A344623 A344624 A344625 * A344627 A344628 A344629

KEYWORD

nonn,base

AUTHOR

Felix Fröhlich, May 25 2021

STATUS

approved

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Last modified December 2 07:33 EST 2021. Contains 349437 sequences. (Running on oeis4.)