A283802 Numbers k such that the concatenation of the first k odd composite numbers is a prime.

21, 73, 132

Offset: 1

Author

XU Pingya, Mar 17 2017

Keywords

• base
• nonn
• bref
• more

Comments

Indices k for which A283801(k) is prime.

A283801(21) = 91521252733353945495155576365697577818587 is a 41-digit prime;

A283801(73) = 91521...247249253 is a 193-digit prime;

A283801(132) = 91521...423425427 is a 370-digit prime.

Next term, if it exists, will be more than 5028.

a(4) > 25000, if it exists. - Michael S. Branicky, Apr 30 2025

Links

• Eric Weisstein's World of Mathematics, Consecutive Number Sequences

Crossrefs

Cf. A007908, A019518, A046035, A069151, A071904, A283801.

Programs

Mathematica

k = 2; cc = oc = 0; lst = {}; While[k < 428, If[OddQ@k && !PrimeQ@k, cc = cc*10^IntegerLength@k + k; oc++; If[PrimeQ[cc], AppendTo[lst, oc]]]; k++]; lst  (* Robert G. Wilson v, Mar 18 2017 *)
Module[{nn=501,ocm},ocm=Select[Range[9,nn,2],CompositeQ];Select[ Range[ Length[ ocm]],PrimeQ[FromDigits[Flatten[IntegerDigits/@Take[ocm,#]]]]&]] (* Harvey P. Dale, Sep 02 2022 *)