A083969 Numbers n such that 2.n.3.n.5.n.7.n.11 is prime (dot means concatenation).

4, 18, 33, 42, 43, 57, 73, 76, 78, 87, 91, 93, 97, 102, 112, 114, 120, 141, 151, 177, 186, 193, 196, 219, 261, 267, 276, 280, 300, 307, 318, 322, 342, 352, 364, 366, 402, 435, 438, 445, 457, 462, 468, 484, 511, 580, 582, 633, 646, 651, 679, 706, 745, 774, 783

Offset: 1

Author

Farideh Firoozbakht, Jun 19 2003

Keywords

• base
• easy
• nonn

Examples

			2.4.3.4.5.4.7.4.11 = 2434547411, which is prime. Hence 4 is in the sequence.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A083677, A032711, A092115, A092117.

Programs

Mathematica

v={};Do[If[PrimeQ[FromDigits[Join[{2}, IntegerDigits[n], {3}, IntegerDigits[n], {5}, IntegerDigits[n], {7}, IntegerDigits[n], {1, 1}]]], v=Append[v, n]], {n, 1000}];v
Select[Range[660], PrimeQ[FromDigits[Join[{2}, IntegerDigits[ # ], {3}, IntegerDigits[ # ], {5}, IntegerDigits[ # ], {7}, IntegerDigits[ # ], {1, 1}]]] &] (* Stefan Steinerberger, Jun 28 2007 *)

Python

from sympy import isprime
def aupton(terms):
  n, alst = 1, []
  while len(alst) < terms:
    s = str(n)
    t = int('2'+s+'3'+s+'5'+s+'7'+s+'11')
    if isprime(t): alst.append(n)
    n += 1
  return alst
print(aupton(55)) # Michael S. Branicky, Apr 18 2021

Extensions

Edited by Stefan Steinerberger, Jun 28 2007

Edited by N. J. A. Sloane, Sep 18 2008 at the suggestion of R. J. Mathar