A083750 Numbers k such that 2111131111...p(k-1)1111p(k) is prime.

1, 85, 145, 304, 915

Offset

1,2

Comments

From Charles R Greathouse IV, Oct 12 2009: (Start)

Let f(k,m) be the decimal concatenation of f(k-1,m), m, and prime(k) for k > 1, and f(1,m) = 2. Then k is in the sequence if f(k, 1111) is prime.

No more terms up to 6300. (End)

No more terms up to 12500. - Michael S. Branicky, Feb 11 2026

Links

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

Carlos Rivera, Puzzle 208.  Happy new Year 2003!, The Prime Puzzles & Problems Connection.

Example

a(2) = 85 is a term because f(85,1111) = 211113111151111...4331111439 is prime and f(k,1111) is composite for 1 < k < 85 (prime(85) = 439).
a(4) = 304 is a term because f(304,1111) = 211113111151111...199911112003 is prime (prime(304) = 2003).

Maple

p:= proc(n) option remember; `if`(n=1, 2,
      parse(cat("", p(n-1), "1111", ithprime(n))))
    end:
select(k-> isprime(p(k)), [$1..305])[];  # Alois P. Heinz, Feb 11 2026

Crossrefs

Cf. A083677, A082549.

Sequence in context: A052479 A239527 A029471 * A043684 A382631 A043574

Adjacent sequences: A083747 A083748 A083749 * A083751 A083752 A083753

Keyword

nonn,base,hard,less,more

Author

Farideh Firoozbakht, Jun 17 2003

Extensions

a(1) = 1 prepended and sequence revised by Sean A. Irvine, Feb 09 2026

Status

approved