A092115 -id:A092115 - cp's OEIS frontend

A092117 Numbers n such that the concatenation 2n3n5n7n11n13 is prime.

10, 43, 51, 55, 58, 60, 136, 171, 204, 213, 214, 222, 270, 288, 309, 334, 339, 364, 366, 376, 414, 423, 460, 477, 492, 501, 502, 507, 513, 519, 565, 585, 586, 597, 621, 649, 726, 729, 787, 852, 861, 870, 903, 906, 915, 933, 946, 981, 988, 1005, 1038, 1071

Offset: 1

Farideh Firoozbakht, Jun 15 2003

This concatenation is fp(6, n) as defined in A083677.

			10 is in the sequence because 210310510710111013 is prime.

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

Cf. A032711, A083677, A083966, A083677, A092115, A083969.

v={};Do[If[PrimeQ[FromDigits[Join[{2}, IntegerDigits[n], {3}, IntegerDigits[n], {5}, IntegerDigits[n], {7}, IntegerDigits[n], {1, 1}, IntegerDigits[n], {1, 3}]]], v=Append[v, n]], {n, 1400}];v
fp6Q[n_] := PrimeQ[ FromDigits[ Flatten[ IntegerDigits /@ Insert[{2, 3, 5, 7, 11, 13}, n, {{2}, {3}, {4}, {5}, {6}}]]]]; Select[ Range[1100], fp6Q[ # ] &] (* Robert G. Wilson v, Dec 11 2004 *)
Select[Range[1100],PrimeQ[FromDigits[Flatten[IntegerDigits/@Riffle[{2,3,5,7,11,13}, #]]]]&] (* Harvey P. Dale, Mar 21 2013 *)

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 27 2007

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

Original entry on oeis.org

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

Farideh Firoozbakht, Jun 19 2003

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

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

Cf. A083677, A032711, A092115, A092117.

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 *)

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

Edited by Stefan Steinerberger, Jun 28 2007

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

cp's OEIS Frontend

A092117 Numbers n such that the concatenation 2n3n5n7n11n13 is prime.

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