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A274134 Primes p such that both ror(p) and rol(p) are also primes, where ror(x)=A038572(x) is x rotated one binary place to the right, rol(x)=A006257(x) is x rotated one binary place to the left. 0
3, 7, 11, 31, 43, 67, 79, 127, 131, 139, 167, 191, 211, 223, 227, 307, 331, 367, 487, 523, 631, 691, 743, 751, 883, 971, 1039, 1087, 1399, 2063, 2083, 2143, 2179, 2239, 2267, 2287, 2347, 2411, 2423, 2503, 2531, 2543, 2591, 2687, 2731, 2803, 2819, 2927, 2939, 2963 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) mod 4 = 3.

LINKS

Table of n, a(n) for n=1..50.

MATHEMATICA

Select[Prime@ Range@ 430, And[PrimeQ@ FromDigits[RotateLeft@ #, 2], PrimeQ@ FromDigits[RotateRight@ #, 2]] &@ IntegerDigits[#, 2] &] (* Michael De Vlieger, Jun 22 2016 *)

PROG

(Python)

from sympy import isprime

for n in range(3, 10000, 2):

    if not isprime(n): continue

    BL = len(bin(n))-2

    x = (n>>1) + ((n&1) << (BL-1))   # A038572(n)

    if not isprime(x): continue

    y = (n*2) - (1<<BL) + 1   # A006257(n)  for n>0

    if not isprime(y): continue

    print str(n)+', ',

CROSSREFS

Cf. A000040, A006257, A038572.

Sequence in context: A213740 A267357 A152084 * A131588 A091938 A333424

Adjacent sequences:  A274131 A274132 A274133 * A274135 A274136 A274137

KEYWORD

nonn,base

AUTHOR

Alex Ratushnyak, Jun 10 2016

STATUS

approved

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Last modified December 9 03:42 EST 2021. Contains 349625 sequences. (Running on oeis4.)