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A168327 Primes of concatenated form "1 n^3". 16
11, 127, 12197, 135937, 159319, 11092727, 11295029, 11860867, 12685619, 14330747, 14826809, 15000211, 15929741, 16128487, 18869743, 19393931, 124137569, 126198073, 127818127, 129503629, 138958219, 150243409, 154439939 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

(1) It is conjectured that sequence is infinite.

(2) These are primes all with "leading" digit "1", they are concatenations of two cubic numbers: 1^3 and n^3, n is a natural.

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

Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

FORMULA

If n^3 is a d-digit number and d no multiple of 3, then p=10^d+n^3, where n is odd and no multiple of 5.

a(n) = c+10^A055642(c) where c=A167725(n). [From R. J. Mathar, Nov 23 2009]

EXAMPLE

(1) 10^1+1^3=11 = prime(5) = a(1).

(2) 10^2+3^3=127 = prime(31) = a(2).

(3) 10^4+13^3=12197 = prime(1458) = a(3).

MATHEMATICA

Select[FromDigits[Join[{1}, IntegerDigits[#]]]&/@(Range[500]^3), PrimeQ] Harvey P. Dale, May 16 2012

CROSSREFS

Cf. A168147, A167535.

Sequence in context: A065543 A015598 A181012 * A282042 A015601 A024144

Adjacent sequences:  A168324 A168325 A168326 * A168328 A168329 A168330

KEYWORD

nonn,base

AUTHOR

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 23 2009

EXTENSIONS

Edited by Charles R Greathouse IV, Apr 24 2010

STATUS

approved

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Last modified August 24 05:52 EDT 2019. Contains 326260 sequences. (Running on oeis4.)