A089056 Primes whose sum of digits [s(d)] is a prime and where sum of two such consecutive s(d) values is a square.

7, 11, 23, 29, 41, 131, 137, 197, 199, 467, 487, 557, 577, 593, 757, 773, 827, 829, 863, 881, 883, 937, 953, 1013, 1019, 1031, 1103, 1109, 1277, 1279, 1567, 1583, 1637, 1657, 1871, 1873, 2003, 2027, 2087, 2089, 2267, 2269, 2377, 2393, 2447, 2467, 2591, 2593

Offset

1,1

Comments

Subsequence of A046704.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

From the sequence of primes whose s(d) values are prime, select those where sum of two consecutive s(d) values is a square.

Example

a(2)=23; a(3)=29: 2+3=5; 2+9=11; 5+11=16, a square.

Mathematica

Module[{sdp=Select[Prime[Range[500]], PrimeQ[Total[IntegerDigits[#]]]&]}, Flatten[Select[ Partition[ sdp, 2, 1], IntegerQ[ Sqrt[ Total[ Flatten[ IntegerDigits/@ #]]]]&]]]//Union (* Harvey P. Dale, Oct 09 2023 *)

Crossrefs

Cf. A046704.

Sequence in context: A182569 A067790 A271043 * A210981 A372303 A255769

Adjacent sequences: A089053 A089054 A089055 * A089057 A089058 A089059

Keyword

easy,nonn,base

Author

Enoch Haga, Dec 20 2003

Extensions

Edited, corrected and extended by Ray Chandler, Feb 14 2004

Status

approved