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A007488 Primes whose reversal is a square.
(Formerly M5321)
28
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

REFERENCES

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.

LINKS

David A. Corneth, Table of n, a(n) for n = 1..14356 (first 1000 terms from T. D. Noe, next 773 terms by Marius A. Burtea)

EXAMPLE

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.

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 *)

PROG

(Python)

from gmpy2 import is_square

from sympy import prime

A007488 = [prime(n) for n in xrange(1, 10**6) if is_square(int(str(prime(n))[::-1]))] # Chai Wah Wu, Aug 14 2014

(PARI) is(n)=isprime(n) && issquare(fromdigits(Vecrev(digits(n)))) \\ Charles R Greathouse IV, Feb 06 2017

(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

CROSSREFS

Cf. A059007, A068989. See A132388 for another version.

For prime reversals that are cubes, 4th powers, 5th powers, see A057699, A058996, A059000. - R. J. Mathar, Nov 13 2007

Sequence in context: A161853 A106096 A142482 * A142538 A057216 A139993

Adjacent sequences:  A007485 A007486 A007487 * A007489 A007490 A007491

KEYWORD

base,nonn,nice

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

STATUS

approved

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Last modified October 18 08:08 EDT 2019. Contains 328146 sequences. (Running on oeis4.)