A242988 Numbers n such that concatenating 1 with three instances of n produces a prime.

7, 9, 21, 39, 53, 57, 61, 63, 67, 69, 139, 149, 161, 163, 173, 187, 189, 201, 207, 219, 233, 247, 259, 269, 273, 279, 291, 293, 299, 301, 347, 363, 413, 447, 451, 453, 467, 473, 481, 511, 531, 537, 539, 549, 583, 609, 623, 629, 633, 637, 649, 663, 691, 697

Offset

1,1

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Example

39 is included because 1393939 is a prime.

Mathematica

cQ[n_, i_]:=Module[{idn=IntegerDigits[n]}, PrimeQ[FromDigits[Flatten[ Join[ {1}, Table[idn, {i}]]]]]]; Select[Range[1000], cQ[#, 3]&]
c13nQ[n_]:=PrimeQ[FromDigits[PadRight[{1}, 3 IntegerLength[n]+1, RotateRight[ IntegerDigits[n]]]]]; Select[Range[700], c13nQ] (* Harvey P. Dale, Aug 14 2017 *)

Prog

(Python)
from sympy import isprime
for n in range(10**3):
..if isprime(int('1'+3*str(n))):
....print(n, end=', ')
# Derek Orr, Aug 17 2014
(PARI) s=[]; for(n=1, 10^3, d=length(Str(n)); if(isprime(10^(3*d)+(10^(3*d)-1)/(10^d-1)*n), s=concat(s, n))); s \\ Jens Kruse Andersen, Aug 18 2014

Crossrefs

Cf. A242987, A242989, A242990.

Sequence in context: A147068 A147012 A032394 * A063486 A070423 A018882

Adjacent sequences: A242985 A242986 A242987 * A242989 A242990 A242991

Keyword

nonn,base,easy

Author

Harvey P. Dale, Aug 17 2014

Status

approved