A007488 Primes whose reversal is a square.
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
Offset: 1
Examples
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.
References
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 113.
- Charles W. Trigg, Primes with Reverses That Are Powers, J. Rec. Math., 17 (1985), 172-176.
Links
- David A. Corneth, Table of n, a(n) for n = 1..14356 (terms 1..1000 from T. D. Noe, terms 1001..1773 from Marius A. Burtea)
Crossrefs
Programs
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Magma
[p: p in PrimesUpTo(150000)|IsSquare(Seqint(Reverse(Intseq(p))))];// Marius A. Burtea, Jan 12 2019
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Maple
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 -
Mathematica
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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PARI
is(n)=isprime(n) && issquare(fromdigits(Vecrev(digits(n)))) \\ Charles R Greathouse IV, Feb 06 2017
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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 -
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
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