A174402 Primes such that applying "reverse and add" twice produces two more primes

271, 281, 21491, 21991, 22091, 22481, 23081, 23971, 24071, 25951, 26681, 26981, 27271, 27431, 27691, 27791, 28031, 28661, 28921, 28961, 29021, 29191, 29251, 29411, 29671, 2129891, 2131991, 2141791, 2141891, 2151791, 2157091, 2161591, 2179391, 2191291

Offset

1,1

Comments

Some observations:

1. For all terms, the first digit is 2, last digit is 1, number of digits is odd: 3,5,7,...

2. The sequence is infinite. Number of 3-digit terms is 2, number of 5-digit terms is 23, number of 7-digit terms is 585, number of 9-digit terms is 26611.

3. Applying "reverse and add" a third time always produces composites. - Zak Seidov, Dec 09 2013

Links

Harvey P. Dale, Table of n, a(n) for n = 1..610 (* All terms with 7 or fewer digits. *)

Example

21491 is included because (1) it is prime, and (2) 21491 + 19412 = 40903 which is prime, and (3) 40903 + 30904 = 71807 which also is prime.

Mathematica

Transpose[Select[Table[{Prime[i], And@@PrimeQ/@NestList[#+FromDigits[ Reverse[ IntegerDigits[#]]]&, Prime[i], 2]}, {i, 500000}], #[[2]] == True&]][[1]]
tmpQ[p_]:=AllTrue[Rest[NestList[#+IntegerReverse[#]&, p, 2]], PrimeQ]; Select[Prime[Range[163000]], tmpQ] (* Harvey P. Dale, Feb 05 2025 *)

Crossrefs

Cf. A061783.

Sequence in context: A290643 A104844 A086003 * A048295 A257210 A020363

Adjacent sequences: A174399 A174400 A174401 * A174403 A174404 A174405

Keyword

nonn,base

Author

Harvey P. Dale, Nov 27 2010

Status

approved