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A176781 Smallest prime prime(i) such that concatenation 2//0_(n)//prime(i) is prime. 1
3, 11, 3, 17, 3, 3, 3, 11, 89, 41, 257, 3, 29, 131, 353, 3, 3, 11, 89, 521, 257, 3, 17, 3, 467, 89, 149, 17, 71, 47, 293, 17, 191, 47, 3, 41, 23, 11, 401, 41, 443, 41, 293, 479, 311, 23, 587, 41, 1289, 1013, 29, 41, 59, 293, 1031, 17, 23, 17, 347, 401, 599, 11, 227, 827, 401 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
We search for the prime such that the first prime (=2) concatenated with n zeros and concatenated with that prime is again a prime number.
If p = prime(i) is a d(i)-digit prime: q = 2 * 10^(n+d(i)) + p has to be prime.
Necessarily prime(i) is congruent to 2 (mod 3).
It is conjectured that prime(i) = 3 occurs infinitely often: at n= 0, 2, 4, 5, 6, 11, 15, 16, 21, 23, 34, 114, 119,...
REFERENCES
E. I. Ignatjew, Mathematische Spielereien, Urania Verlag Leipzig/Jena/ Berlin 1982
LINKS
EXAMPLE
n = 0: 2//3 = 23 = prime(9), 3 = prime(2) is first term
n = 1: 2//0//11 = 2011 = prime(305), 11 = prime(5) is 2nd term
n = 2: 2//00//3 = 2003 = prime(304), 3 = prime(2) is 3rd term
CROSSREFS
Sequence in context: A303114 A359990 A170856 * A349407 A306367 A226625
KEYWORD
base,nonn
AUTHOR
Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 26 2010
EXTENSIONS
Offset corrected and sequence extended by R. J. Mathar, Apr 28 2010
STATUS
approved

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Last modified July 12 11:28 EDT 2024. Contains 374245 sequences. (Running on oeis4.)