A168375 Natural numbers n for which the concatenation "1 n^3" (A168327) is prime.

1, 3, 13, 33, 39, 103, 109, 123, 139, 163, 169, 171, 181, 183, 207, 211, 289, 297, 303, 309, 339, 369, 379, 393, 423, 451, 457, 463, 1021, 1027, 1047, 1053, 1057, 1081, 1087, 1111, 1123, 1161, 1189, 1201, 1249, 1273, 1293, 1303, 1329, 1339, 1351, 1381, 1387

Offset

1,2

Comments

It is conjectured that the sequence is infinite.

All terms are odd. - Harvey P. Dale, Sep 26 2025

References

Harold Davenport, Multiplicative Number Theory, Springer-Verlag New-York 1980

Friedhelm Padberg, Elementare Zahlentheorie, Spektrum Akademischer Verlag, 2. Auflage 1991

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

Links

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

Example

(1) "1 1^3"=10^1+1^3=11=prime(5) gives a(1)=1.
(2) "1 3^3"=10^2+3^3=127=prime(31) gives a(2)=3.
(3) "1 13^3"=10^4+13^3=12197=prime(1458) gives a(3)=13.

Maple

q:= n-> isprime(parse(cat(1, n^3))):
select(q, [1+2*i$i=0..750])[];  # Alois P. Heinz, Sep 26 2025

Mathematica

Select[Range[1, 1500, 2], With[{c=#^3}, PrimeQ[10^IntegerLength[c]+c]]&] (* Harvey P. Dale, Sep 26 2025 *)

Crossrefs

Cf. A000040 The prime numbers.

Cf. A168147 Primes of the form p = 1 + 10*n^3 for a natural number n.

Cf. A168327 Primes of concatenated form p= "1 n^3".

Cf. A167535 Concatenation of two square numbers which give a prime.

Sequence in context: A211800 A218922 A061938 * A032586 A147137 A146230

Adjacent sequences: A168372 A168373 A168374 * A168376 A168377 A168378

Keyword

nonn,base

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 24 2009

Extensions

Edited by Charles R Greathouse IV, Apr 23 2010

Status

approved