A173874 Primes in A173836.

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

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: A357175 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