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 A168147 Primes of the form 10*n^3 + 1. 15
 11, 271, 641, 2161, 33751, 40961, 58321, 138241, 196831, 270001, 297911, 466561, 506531, 795071, 1326511, 1406081, 1851931, 2160001, 3890171, 4218751, 5314411, 5513681, 6585031, 7290001, 8043571, 11910161, 12597121, 12950291, 14815441 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS (1) These primes all with end digit 1=1^3 are concatenations of two CUBIC numbers: "n^3 1". (2) It is conjectured that the sequence is infinite. (3) It is an open problem if 3 consecutive naturals n exist which give such a prime. No three such integers exist, as every n = 2 (mod 3) yields 10n^3 + 1 = 0 (mod 3). - Charles R Greathouse IV, Apr 24 2010 REFERENCES Harold Davenport, Multiplicative Number Theory, Springer-Verlag New-York 1980 Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 FORMULA a(n) = 10*A168219(n)^3 + 1.  \\ M. F. Hasler, Jul 24 2011 MATHEMATICA Select[Table[10*n^3+1, {n, 1000}], PrimeQ] (* Vincenzo Librandi, Aug 01 2012 *) PROG (PARI) for(n=1, 2e2, isprime(n^3*10+1) && print1(n^3*10+1", "))  \\ M. F. Hasler, Jul 24 2011 (MAGMA) [ a: n in [1..150] | IsPrime(a) where a is 10*n^3+1 ]; // Vincenzo Librandi, Jul 25 2011 CROSSREFS Cf. A030430 (primes of the form 10*n+1). Cf. A167535 (concatenation of two square numbers which give a prime). See A168219 for the numbers n. Sequence in context: A255955 A285051 A267900 * A108519 A160195 A203240 Adjacent sequences:  A168144 A168145 A168146 * A168148 A168149 A168150 KEYWORD nonn,base,easy AUTHOR Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 19 2009 STATUS approved

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Last modified January 28 13:29 EST 2020. Contains 331321 sequences. (Running on oeis4.)