A176371 - OEIS

%I #13 Dec 18 2015 03:37:57

%S 31,41,71,83,281,311,431,479,733,751,797,2011,2857,3163,4373,4397,

%T 4943,7541,7577,7583,9413,9491,20533,20731,20771,24151,24547,24767,

%U 26249,28979,31121,41201,41609,43321,43391,43753,45641,49459,49463,49811,49891

%N Primes p such that reversal(p) - 13 is a square.

%C R(n) denotes the Reversal of a natural number n

%C List of all (p,N) for p < 10^6 - 1:

%C (*) for emirp pair (p,R(p)), (+) if square base N is a prime

%C (41,1), (71,2) (+) (*), (83,5) (+), (281,13) (+), (311,10) (*), (431,11) (+), (479,31) (+), (733,18) (*), (751,12) (*), (797,28),

%C (2011,33), (2857,87), (4373,61) (+), (4397,89) (+), (4943,59) (+), (7541,38), (7577,88) (*), (7583,62), (9413,56), (9491,44) (*), (20533,183), (20731,117), (20771,133), (24151,123), (24547,273), (24767,277) (+), (26249,307) (+), (28979,313) (+), (31121,110) (*), (41201,101) (+),

%C (41609,301), (43321,111), (43391,139) (+), (43753,189), (45641,121), (49459,309), (49463,191) (+), (49811,109), (49891,141), (71293,198) (*),

%C (73133,182), (73471,132), (73597,282) (*), (75521,112), (77611,108) (*), (77849,308), (77863,192) (*), (79613,178), (79841,122) (*), (83207,265),

%C (83231,115), (83243,185), (83299,315), (90031,114) (*), (92801,104), (96431,116) (*), (98057,274)

%D W. W. R. Ball, H. S. M.Coxeter: Mathematical Recreations and Essays, Dover Publications, 13th edition, 1987

%D O. Fritsche, R. Mischak and T. Krome: Verflixt und zugeknobelt, Mehr mathematische Raetselgeschichten, Rowohlt TB. Nr.62190, 2007

%D C. W. Trigg, Primes with Reverses That Are Powers, J. Rec. Math. 17, 1985

%H Chai Wah Wu, <a href="/A176371/b176371.txt">Table of n, a(n) for n = 1..7605</a>

%e 41 = prime(13), R(41) - 13 = 14 - 13 = 1^2, is a term.

%e 71 = prime(20), 17 - 13 = 2^2, is a term.

%e 83 = prime(23), 38 - 13 = 5^2, is a term.

%e 797 = prime(139) = palindromic prime(18), N = 28^2, is also a term.

%e Note successive terms that are also consecutive primes: p(17) = 7577, p(18) = 7583, p(36) = 49459, p(37) = 49463, p(46) = 77849, p(47) = 77863.

%o (PARI) isok(n) = {if (! isprime(n), return (0)); d = digits(n); revn = sum(i=1, #d, d[i]*10^(i - 1)); issquare(revn-13);} \\ _Michel Marcus_, Aug 25 2013

%o (Python)

%o from sympy import isprime

%o A176371_list, i, j = [], 0, 13

%o while j < 10**10:

%o     p = int(str(j)[::-1])

%o     if j % 10 and isprime(p):

%o         A176371_list.append(p)

%o     j += 2*i+1

%o     i += 1

%o A176371_list = sorted(A176371_list) # _Chai Wah Wu_, Dec 17 2015

%Y Cf. A000040, A000290, A002385, A006567, A007488.

%K base,nonn

%O 1,1

%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 16 2010

%E Two more terms 31 and 3163 added by _Michel Marcus_, Aug 25 2013