A173733 -id:A173733 - cp's OEIS frontend

A173836 Natural numbers n such that the concatenation 1331//n^3 is a prime number.

21, 27, 29, 41, 101, 119, 141, 171, 173, 177, 191, 197, 219, 243, 267, 291, 309, 327, 333, 369, 371, 383, 411, 417, 1019, 1049, 1059, 1091, 1157, 1163, 1211, 1311, 1337, 1343, 1359, 1371, 1379, 1409, 1461, 1473, 1481, 1503, 1521, 1593, 1599, 1613, 1637

Offset: 1

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Feb 26 2010

Given the cube n^3 with k = A111393(n) decimal digits, we have to check whether the concatenation, 11^3 * 10^k + n^3, is a prime.
The number k of digits that 1331=11^3 is shifted is not a multiple of 3,
because the form a^3+b^3 = (a^2+a*b+b^2) * (a - b) cannot construct a prime.

			21 is in the sequence because 21^3=9261, and the concatenation is 13319261=prime(868687).
27 is in the sequence because 27^3=19683, and the concatenation is 133119683=prime(7545064).

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

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

Cf. A102006, A167535, A168147, A168219, A168274, A173579, A173733

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

Comments sligthly rephrased - R. J. Mathar, Mar 05 2010

A173874 Primes in A173836.

Original entry on oeis.org

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

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

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).

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

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

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

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

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

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

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

cp's OEIS Frontend

A173836 Natural numbers n such that the concatenation 1331//n^3 is a prime number.

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