A173579 Natural numbers n which give primes when 1331 = 11^3 is prefixed.

3, 17, 21, 53, 57, 69, 83, 87, 107, 119, 123, 153, 207, 227, 243, 249, 251, 261, 269, 279, 293, 299, 327, 329, 333, 339, 347, 377, 381, 383, 399, 411, 431, 437, 443, 471, 489, 497, 513, 521, 527, 549, 567, 573, 579, 587, 591, 597, 599, 611, 633, 641, 647, 657

Offset: 1

Author

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

Keywords

• base
• nonn

Comments

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

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

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.

Examples

			13313 = prime(1581) => a(1) = 3.
133117 = prime(12425) => a(2) = 17.
133103, 133109 are prime, but "0" included: "03" resp. "09" are no terms of the sequence.
		

References

• Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005
• K. Haase, P. Mauksch: Spass mit Mathe, Urania-Verlag Leipzig, Verlag Dausien Hanau, 2. Auflage 1985
• Theo Kempermann: Zahlentheoretische Kostproben, Harri Deutsch, 2. aktualisierte Auflage 2005

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

A102006, A167535, A168147, A168219, A168274

Programs

Mathematica

Select[Range[700],PrimeQ[1331*10^IntegerLength[#]+#]&] (* Harvey P. Dale, Jun 25 2020 *)

PARI

isok(n) = isprime(n + 1331*10^(length(Str(n)))); \\ Michel Marcus, Aug 27 2013