The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A178316 Primes whose digital rotation is still prime. 3
 2, 5, 11, 19, 61, 101, 109, 151, 181, 199, 601, 619, 659, 661, 1019, 1021, 1061, 1091, 1109, 1129, 1151, 1181, 1201, 1229, 1259, 1291, 1511, 1559, 1601, 1609, 1621, 1669, 1699, 1811, 1901, 1999, 6011, 6091, 6101, 6199, 6211, 6221, 6229, 6521, 6551, 6569 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This means if written as in a digital clock and rotated 180 degrees around the center the result is also prime (possibly a different prime). REFERENCES Guy, R. K., Unsolved Problems in Number Theory, p 15 This sequence is related to the palindromic primes with symmetries as in Guy's book. LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 EXAMPLE For example 1259 becomes 6521 under such a rotation. MATHEMATICA Select[Range[6570], PrimeQ[#]&&PrimeQ[FromDigits[Reverse[IntegerDigits[#]/.{6->9, 9->6}]]]&&ContainsOnly[IntegerDigits[#], {0, 1, 2, 5, 6, 8, 9}]&] (* James C. McMahon, Apr 09 2024 *) PROG (Python) from itertools import count, islice, product from sympy import isprime def A178316_gen(): yield from (2, 5) r = ''.maketrans('69', '96') for l in count(1): for a in '125689': for d in product('0125689', repeat=l): s = a+''.join(d) m = int(s) if isprime(m) and isprime(int(s[::-1].translate(r))): yield m A178316_list = list(islice(A178316_gen(), 40)) # Chai Wah Wu, Apr 09 2024 CROSSREFS Cf. A007500, A055387, A018847. Sequence in context: A276591 A051653 A106015 * A179632 A093871 A139482 Adjacent sequences: A178313 A178314 A178315 * A178317 A178318 A178319 KEYWORD nonn,base AUTHOR David Nacin, May 24 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 18 20:35 EDT 2024. Contains 376002 sequences. (Running on oeis4.)