A086244 Primes such that a sum of any two adjacent digits is prime; first and last digits are considered adjacent.

11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 211, 2029, 2111, 2129, 2141, 2143, 2161, 2341, 2383, 2389, 2503, 2521, 4111, 4129, 4349, 4703, 4943, 6121, 6521, 6761, 8329, 8389, 8923, 8929, 11161, 11411, 12161, 12941, 14321, 14341, 14741, 16111, 16141, 16561, 16741, 20323, 20341, 20389, 20521

Offset

1,1

Comments

Each (2- or more-digit) term must begin with one of the even digits 2,4,6,8 or else must begin and end with the digit 1. All repunit primes (A004022) are terms as the sums are always 2.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 623 terms from Zak Seidov)

Example

2029 is a term because it is a prime and 2+0, 0+2, 2+9, 9+2 are all primes.

Mathematica

p=10; Reap[Do[Label[ne]; p=NextPrime[p]; id=IntegerDigits[p];
   id1=Append[id, id[[1]]]; id2=Prepend[id, id[[-1]]];
   If[{True}==Union[PrimeQ[id1+id2]], Sow[p]], {2000}]][[2, 1]]
(* Zak Seidov, May 10 2016 *)
tadpQ[n_]:=Module[{idn=IntegerDigits[n]}, AllTrue[ Join[{idn[[1]]+ idn[[-1]]}, Total/@Partition[idn, 2, 1]], PrimeQ]]; Select[Prime[Range[ 2500]], tadpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 08 2019 *)

Crossrefs

Sequence in context: A091367 A088136 A164932 * A091939 A072185 A105898

Adjacent sequences: A086241 A086242 A086243 * A086245 A086246 A086247

Keyword

easy,base,nonn

Author

Zak Seidov, Jul 13 2003

Extensions

Corrected and extended by Rick L. Shepherd, Feb 11 2004

Status

approved