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A007488
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Primes whose reversal is a square.
(Formerly M5321)
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26
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61, 163, 487, 691, 1297, 1861, 4201, 4441, 4483, 5209, 5227, 9049, 9631, 12391, 14437, 16141, 16987, 61483, 63211, 65707, 65899, 67057, 69481, 92767, 94273, 96979, 106303, 108061, 123031, 123373, 125329, 127291, 129643, 142771, 146857, 148249, 165901
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OFFSET
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1,1
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COMMENTS
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Number of terms less than 10^k: 0, 0, 1, 4, 13, 26, 74, 213, 615, 1773, 5000, 14356, 41474, 120186, 352310, 1035235, ... - Muniru A Asiru, Jan 19 2018 and David A. Corneth, Jan 12 2019
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Charles W. Trigg, Primes with Reverses That Are Powers, J. Rec. Math., 17 (1985), 172-176.
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LINKS
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EXAMPLE
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61 is in the sequence because 16 = 4^2.
163 is in the sequence because 361 = 19^2.
167 is not in the sequence because 761 is also prime, not a square.
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MAPLE
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revdigs:= proc(n)
local L, nL, j;
L:= convert(n, base, 10);
nL:= nops(L);
add(L[i]*10^(nL-i), i=1..nL);
end:
map(proc(i) local r; r:= revdigs(i^2); if isprime(r) then r else NULL fi end proc, {$1..9999}); # Robert Israel, Aug 14 2014
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MATHEMATICA
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Select[Prime[Range[16000]], IntegerQ[Sqrt[ToExpression[StringReverse[ToString[#]]]]] &]
Select[Prime[Range[16000]], IntegerQ[Sqrt[FromDigits[ Reverse[ IntegerDigits[ #]]]]] &] (* Harvey P. Dale, Jul 19 2011 *)
Select[Prime@ Range[10^5], IntegerQ@ Sqrt@ IntegerReverse@ # &] (* Michael De Vlieger, Jan 20 2018 *)
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PROG
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(Python)
from gmpy2 import is_square
from sympy import prime
A007488 = [prime(n) for n in range(1, 10**6) if is_square(int(str(prime(n))[::-1]))] # Chai Wah Wu, Aug 14 2014
(PARI) uptoQdigits(n) = {my(res=List(), i2); for(i=4, sqrtint(10^n), i2 = i^2; if(i%10!=0 && gcd(10, i2 \ (10^logint(i2, 10))) == 1, c=fromdigits(Vecrev(digits(i2))); if(isprime(c), listput(res, c) ) ) ); listsort(res); res } \\ David A. Corneth, Jan 12 2019
(Magma) [p: p in PrimesUpTo(150000)|IsSquare(Seqint(Reverse(Intseq(p))))]; // Marius A. Burtea, Jan 12 2019
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CROSSREFS
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KEYWORD
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base,nonn,nice
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AUTHOR
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STATUS
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approved
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