A326317 Lexicographically earliest sequence of distinct terms such that the digits of a(n) and a(n+1) sum up to a square and a(n) + a(n+1) is also a square.

1, 3, 6, 19, 150, 46, 123, 21, 15, 154, 42, 102, 67, 129, 40, 41, 103, 66, 130, 14, 22, 122, 47, 149, 20, 16, 9, 7, 2, 34, 110, 11, 25, 144, 52, 117, 79, 90, 106, 63, 133, 36, 160, 324, 205, 279, 250, 234, 295, 794, 230, 211, 113, 31, 5, 4, 32, 112, 57, 139, 30, 51, 118, 78, 91, 105, 64, 132, 12, 24, 120, 49, 147, 337, 192, 292

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Jun 24 2019

Keywords

• base
• nonn

Examples

			The sequence starts with 1,3,6,19,150,46,123,... and we see indeed that:
the digits of {a(1); a(2)} have sum 1 + 3 = 4 (square) and a(1) + a(2) is a square too (4);
the digits of {a(2); a(3)} have sum 3 + 6 = 9 (square) and a(2) + a(3) is a square too (9);
the digits of {a(3); a(4)} have sum 6 + 1 + 9 = 16 (square) and a(3) + a(4) = 6 + 19 is a square too (25);
the digits of {a(4); a(5)} have sum 1 + 9 + 1 + 5 + 0 = 16 (square) and a(4) + a(5) = 19 + 150 is a square too (169 --> square of 13);
the digits of {a(5); a(6)} have sum 1 + 5 + 0 + 4 + 6  = 16 (square) and a(5) + a(6) = 150 + 46 is a square too (196 --> square of 16);
the digits of {a(6); a(7)} have sum 4 + 6 + 1 + 2 + 3 = 16 (square) and a(6) + a(7) = 46 + 123 is a squaretoo (169);
etc.
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..10001

Crossrefs

Cf. A326315 (replace the word "square" by "palindrome"), A326316 (replace the word "square" by "prime"); in A308727 only the sum of the digits is a square.