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

Author

Harvey P. Dale, Nov 27 2010

Keywords

• nonn
• base

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A061783.

Programs

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 *)