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A173874 Primes in A173836. 1
29, 41, 101, 173, 191, 197, 383, 1019, 1049, 1091, 1163, 1409, 1481, 1613, 1637, 1721, 1823, 1913, 1973, 2027, 2099, 2243, 2339, 2351, 2447, 2729, 2837, 2897, 2999, 3023, 3089, 3137, 3167, 3203, 3251, 3407, 3881, 4019, 4349, 4397, 4451, 4457 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For a prime p and its k-digit cube p^3 we need to check if q = 11^3 * 10^k + p^3 is a prime.

11^3*10^k is congruent to 2 (mod 3), so p^3 must be congruent to 2 (mod 3) because otherwise the sum q cannot become a prime.

In turn, all p in the sequence are also congruent to 2 (mod 3) (see A003627).

REFERENCES

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

LINKS

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

EXAMPLE

The prime 29 is in the sequence because 29^3=24389, and the concatenation 133124389=prime(7545294) is a prime number.

MAPLE

cat2 := proc(a, b) ndgs := max(1, ilog10(b)+1) ; a*10^ndgs+b ; end proc:

for i from 1 to 800 do p := ithprime(i) ; if isprime(cat2(1331, p^3)) then printf("%d, ", p) ; end if; end do: # R. J. Mathar, Mar 26 2010

MATHEMATICA

Select[Prime[Range[2000]], PrimeQ[FromDigits[Join[{1, 3, 3, 1}, IntegerDigits[ #^3]]]]&] (* Harvey P. Dale, Oct 14 2011 *)

CROSSREFS

Cf. A000578, A168147, A168219, A173579, A173733, A173836

Sequence in context: A104072 A070268 A139870 * A308795 A106075 A238666

Adjacent sequences:  A173871 A173872 A173873 * A173875 A173876 A173877

KEYWORD

base,nonn

AUTHOR

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 01 2010

EXTENSIONS

Definition simplified, missing numbers 2243, 2339 etc. inserted, numbers like 2621, 2693 removed - R. J. Mathar, Mar 26 2010

STATUS

approved

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Last modified April 13 15:11 EDT 2021. Contains 342936 sequences. (Running on oeis4.)