A173733 Primes p which give primes when 1331 = 11^3 is prefixed (see A173579).

3, 17, 53, 83, 107, 227, 251, 269, 293, 347, 383, 431, 443, 521, 587, 599, 641, 647, 683, 719, 761, 773, 821, 857, 929, 1031, 1097, 1217, 1223, 1301, 1367, 1409, 1433, 1451, 1619, 1637, 1709, 1787, 1973, 2081, 2087, 2129, 2399, 2477, 2591, 2633, 2657, 2693

Offset

1,1

Comments

N = 1331 = 11^3, p k-digit prime, to check if q = N * 10^k + p is prime

With exception of 3 necessarily p of form 3k+2, as sod(1331 = 8)

References

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

Helmut Kracke, Mathe-musische Knobelisken, Duemmler Bonn, 2. Auflage 1983

Links

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

Example

13313 = prime(1581) => a(1) = prime(2) = 3
133117 = prime(12425) => a(2) = prime(7) = 17
133153 = prime(12427) => a(3) = prime(16) = 53
13311217 = prime(868166) => a(28) = prime(199) = 1217
13311223 = prime(868167) => a(29) = prime(200) = 1223
Note: two consecutive primes P = prime(n), Q = prime(n+1) yield consecutive prime concatenations "N P" = prime(m) and "N Q" = prime(m+1)

Mathematica

Select[Prime[Range[400]], PrimeQ[FromDigits[Join[{1, 3, 3, 1}, IntegerDigits[ #]]]]&] (* Harvey P. Dale, Jun 09 2015 *)

Crossrefs

Cf. A102006, A167535, A168147, A168219, A168274, A173579

Sequence in context: A225727 A163943 A093418 * A294134 A258032 A361525

Adjacent sequences: A173730 A173731 A173732 * A173734 A173735 A173736

Keyword

nonn,base,less

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Feb 23 2010

Extensions

Edited and extended by Charles R Greathouse IV, Apr 24 2010

Status

approved