A276462 Prime numbers that consist of k 2's digits followed by k+1 1's digits for some k >= 1.

211, 22111, 2221111, 22222222222222222222222222111111111111111111111111111, 2222222222222222222222222222222221111111111111111111111111111111111

Offset

1,1

Comments

a(4) is 26 2's followed by 27 1's; a(5) is 33 2's followed by 34 1's.

The sequence is conjectured to be infinite.

Let b(n) be the sequence of corresponding k's. b(1)-b(8) are 1, 2, 3, 26, 33, 215, 259, 799. - Felix Fröhlich, Sep 04 2016

Links

Table of n, a(n) for n=1..5.

Mathematica

Select[FromDigits@ Join[ConstantArray[2, #], ConstantArray[1, # + 1]] & /@ Range@ 36, PrimeQ] (* Michael De Vlieger, Sep 04 2016 *)
Select[Table[FromDigits[Join[PadRight[{}, n, 2], PadRight[{}, n+1, 1]]], {n, 40}], PrimeQ] (* Harvey P. Dale, Mar 02 2023 *)

Prog

(PARI) a002275(n) = (10^n-1)/9
a011557(n) = 10^n
terms(n) = my(i=0, k=1); while(1, my(x=2*a002275(k)*a011557(k+1)+a002275(k+1)); if(ispseudoprime(x), print1(x, ", "); i++); k++; if(i==n, break))
/* Print initial five terms as follows: */
terms(5) \\ Felix Fröhlich, Sep 04 2016

Crossrefs

Cf. A000040 (prime numbers).

Sequence in context: A276461 A093732 A116075 * A096834 A013547 A181002

Adjacent sequences: A276459 A276460 A276461 * A276463 A276464 A276465

Keyword

nonn,base

Author

Bob Selcoe, Sep 03 2016

Status

approved