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A174884
Palindromic primes using only (decimal) square digits 0,1,4,9.
2
11, 101, 191, 919, 11411, 19991, 91019, 94049, 94949, 1114111, 1190911, 1409041, 1411141, 1444441, 1490941, 1909091, 1941491, 9049409, 9091909, 9109019, 9110119, 9149419, 9199919, 9400049, 9414149, 9419149, 9440449, 9919199
OFFSET
1,1
COMMENTS
Four decimal square digits: 0 = 0^2, 1 = 1^2, 4 = 2^2, 9 = 3^2
With the exception of 11 all palindromic primes have an odd number of digits
REFERENCES
Roland Sprague, Unterhaltsame Mathematik, neue Probleme, ueberraschende Loesungen, Vieweg, Braunschweig, 1961
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books: London, 1986.
EXAMPLE
11 = prime(5) = palprime(5), 1st term of sequence.
101 = prime(26) = palprime(6), 2nd term of sequence.
Next term using only 0 and 1 is 100111001 = prime(5767473) = palprime(785).
MATHEMATICA
Select[FromDigits/@Tuples[{0, 1, 4, 9}, 7], PalindromeQ[#]&&PrimeQ[#]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 06 2019 *)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 01 2010
STATUS
approved