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 A176371 Primes p such that reversal(p) - 13 is a square. 4
 31, 41, 71, 83, 281, 311, 431, 479, 733, 751, 797, 2011, 2857, 3163, 4373, 4397, 4943, 7541, 7577, 7583, 9413, 9491, 20533, 20731, 20771, 24151, 24547, 24767, 26249, 28979, 31121, 41201, 41609, 43321, 43391, 43753, 45641, 49459, 49463, 49811, 49891 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS R(n) denotes the Reversal of a natural number n List of all (p,N) for p < 10^6 - 1: (*) for emirp pair (p,R(p)), (+) if square base N is a prime (41,1), (71,2) (+) (*), (83,5) (+), (281,13) (+), (311,10) (*), (431,11) (+), (479,31) (+), (733,18) (*), (751,12) (*), (797,28), (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) (+), (41609,301), (43321,111), (43391,139) (+), (43753,189), (45641,121), (49459,309), (49463,191) (+), (49811,109), (49891,141), (71293,198) (*), (73133,182), (73471,132), (73597,282) (*), (75521,112), (77611,108) (*), (77849,308), (77863,192) (*), (79613,178), (79841,122) (*), (83207,265), (83231,115), (83243,185), (83299,315), (90031,114) (*), (92801,104), (96431,116) (*), (98057,274) REFERENCES W. W. R. Ball, H. S. M.Coxeter: Mathematical Recreations and Essays, Dover Publications, 13th edition, 1987 O. Fritsche, R. Mischak and T. Krome: Verflixt und zugeknobelt, Mehr mathematische Raetselgeschichten, Rowohlt TB. Nr.62190, 2007 C. W. Trigg, Primes with Reverses That Are Powers, J. Rec. Math. 17, 1985 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..7605 EXAMPLE 41 = prime(13), R(41) - 13 = 14 - 13 = 1^2, is a term. 71 = prime(20), 17 - 13 = 2^2, is a term. 83 = prime(23), 38 - 13 = 5^2, is a term. 797 = prime(139) = palindromic prime(18), N = 28^2, is also a term. 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. PROG (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 (Python) from sympy import isprime A176371_list, i, j = [], 0, 13 while j < 10**10:     p = int(str(j)[::-1])     if j % 10 and isprime(p):         A176371_list.append(p)     j += 2*i+1     i += 1 A176371_list = sorted(A176371_list) # Chai Wah Wu, Dec 17 2015 CROSSREFS Cf. A000040, A000290, A002385, A006567, A007488. Sequence in context: A202286 A285805 A141180 * A284531 A040987 A040180 Adjacent sequences:  A176368 A176369 A176370 * A176372 A176373 A176374 KEYWORD base,nonn AUTHOR Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 16 2010 EXTENSIONS Two more terms 31 and 3163 added by Michel Marcus, Aug 25 2013 STATUS approved

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Last modified October 19 03:54 EDT 2019. Contains 328211 sequences. (Running on oeis4.)