A173579 - OEIS

%I #8 Jun 25 2020 12:00:58

%S 3,17,21,53,57,69,83,87,107,119,123,153,207,227,243,249,251,261,269,

%T 279,293,299,327,329,333,339,347,377,381,383,399,411,431,437,443,471,

%U 489,497,513,521,527,549,567,573,579,587,591,597,599,611,633,641,647,657

%N Natural numbers n which give primes when 1331 = 11^3 is prefixed.

%C Concatenation of N = 1331 = 11^3 = palindrome(113) and natural n is a prime. No zeros "between" N and n.

%C 13 = emirp(1) = prime(6), R(13) = 31 = emirp(3) = prime(11).

%C Necessarily n = 3 * k or n = 3 * k + 2, but not n = 3 * k + 1, because sod(1331) = 8. So no prime twins are terms of the sequence.

%D Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005

%D K. Haase, P. Mauksch: Spass mit Mathe, Urania-Verlag Leipzig, Verlag Dausien Hanau, 2. Auflage 1985

%D Theo Kempermann: Zahlentheoretische Kostproben, Harri Deutsch, 2. aktualisierte Auflage 2005

%H Harvey P. Dale, <a href="/A173579/b173579.txt">Table of n, a(n) for n = 1..1000</a>

%e 13313 = prime(1581) => a(1) = 3.

%e 133117 = prime(12425) => a(2) = 17.

%e 133103, 133109 are prime, but "0" included: "03" resp. "09" are no terms of the sequence.

%t Select[Range[700],PrimeQ[1331*10^IntegerLength[#]+#]&] (* _Harvey P. Dale_, Jun 25 2020 *)

%o (PARI) isok(n) = isprime(n + 1331*10^(length(Str(n)))); \\ _Michel Marcus_, Aug 27 2013

%Y A102006, A167535, A168147, A168219, A168274

%K base,nonn

%O 1,1

%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Feb 22 2010