A108659 Square-chain primes (including square-loop primes).

2, 13, 31, 79, 97, 101, 109, 131, 181, 227, 313, 401, 409, 631, 727, 797, 881, 1009, 1013, 1097, 2797, 3109, 3181, 3631, 4001, 4013, 7901, 8101, 9001, 9013, 10009, 10181, 10909, 10979, 13109, 18131, 18181, 22279, 22727, 27901, 31013, 36313

Offset: 1

Author

Zak Seidov, Jun 16 2005

Keywords

• nonn
• base

Comments

Primes such that each pair of adjacent digits sums up to a square. First term is a square-loop prime, cf. A108660.

Crossrefs

Cf. A046704, A007953, A088133, A088134, A088135, A088136, A108660.

Programs

Mathematica

Join[{2},Select[Prime[Range[5,4000]],PrimeQ[#]&&AllTrue[Sqrt[#]&/@(Total/@Partition[ IntegerDigits[ #],2,1]),IntegerQ]&]] (* Harvey P. Dale, Jun 02 2024 *)