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A176838 Primes p such that p^3 = q//3 for a prime q. 2
17, 157, 257, 277, 397, 677, 877, 997, 1217, 1697, 1997, 2417, 2777, 3257, 3517, 3697, 4157, 4177, 5077, 5197, 5897, 6277, 7417, 7517, 8377, 9397, 9497, 9677, 9857, 11197, 11597, 12157, 12457, 12697, 13397, 13477, 13877, 14057, 14197, 15017, 16477, 17597, 18097 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Diophantine equation p^3 = 10 * q + 3 with side condition p and q prime. Necessarily LSD for such primes p is e = 7 and the two Last Significant Digit strings are "17", "57", "77" or "97".

REFERENCES

J.-P. Allouche, J. Shallit: Automatic Sequences, Theory, Applications, Generalizations, Cambridge University Press, 2003

G. H. Hardy, E. M. Wright, E. M., An Introduction to the Theory of Numbers (Fifth edition), Oxford University Press, 1980

F. Padberg: Zahlentheorie und Arithmetik, Spektrum Akademie Verlag, Heidelberg - Berlin 1999

LINKS

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

EXAMPLE

17^3 = 4913 = prime(94)//3, 17 = prime(7) is first term.

157^3 = 3869893 = prime(32838)//3, 157 = prime(37) is second term.

MATHEMATICA

Select[Range[7, 20000, 10], PrimeQ[#]&&PrimeQ[FromDigits[Most[IntegerDigits[ #^3]]]]&] (* Harvey P. Dale, Oct 03 2013 *)

CROSSREFS

Cf. A000040, A000578, A174979.

Sequence in context: A160699 A034272 A142087 * A176622 A125380 A126538

Adjacent sequences:  A176835 A176836 A176837 * A176839 A176840 A176841

KEYWORD

base,nonn

AUTHOR

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 27 2010

STATUS

approved

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Last modified February 25 21:55 EST 2020. Contains 332264 sequences. (Running on oeis4.)