OFFSET
1,1
COMMENTS
The numbers themselves need not be palindromes.
The range is a subset of the range of A071786. - Reinhard Zumkeller, Jul 06 2009
Number of terms less than 10^n: 4, 13, 56, 260, 1759, 11297, 82439, 618017, 4815213, 38434593, ..., . - Robert G. Wilson v, Jan 08 2015
REFERENCES
Roozbeh Hazrat, Mathematica: A Problem-Centered Approach, Springer 2010, pp. 39, 131-132
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 134.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
Cécile Dartyge, Bruno Martin, Joël Rivat, Igor E. Shparlinski, and Cathy Swaenepoel, Reversible primes, arXiv:2309.11380 [math.NT], 2023. See p. 3.
MAPLE
revdigs:= proc(n)
local L, nL, i;
L:= convert(n, base, 10);
nL:= nops(L);
add(L[i]*10^(nL-i), i=1..nL);
end:
Primes:= select(isprime, {2, seq(2*i+1, i=1..5*10^5)}):
Primes intersect map(revdigs, Primes); # Robert Israel, Aug 14 2014
MATHEMATICA
Select[ Prime[ Range[ 168 ] ], PrimeQ[ FromDigits[ Reverse[ IntegerDigits[ # ] ] ] ]& ] (* Zak Seidov, corrected by T. D. Noe *)
Select[Prime[Range[1000]], PrimeQ[IntegerReverse[#]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 15 2016 *)
PROG
(Magma) [ p: p in PrimesUpTo(1030) | IsPrime(Seqint(Reverse(Intseq(p)))) ]; // Bruno Berselli, Jul 08 2011
(Haskell)
a007500 n = a007500_list !! (n-1)
a007500_list = filter ((== 1) . a010051 . a004086) a000040_list
-- Reinhard Zumkeller, Oct 14 2011
(Python)
from sympy import prime, isprime
A007500 = [prime(n) for n in range(1, 10**6) if isprime(int(str(prime(n))[::-1]))] # Chai Wah Wu, Aug 14 2014
CROSSREFS
Cf. A002385 (primes that are palindromes in base 10).
KEYWORD
base,nonn,nice
AUTHOR
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Oct 31 2000
Added further terms to the sequence Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 16 2009. Checked by N. J. A. Sloane, Jan 20 2009.
Third reference added by Harvey P. Dale, Oct 17 2011
STATUS
approved