A030465 Numbers k such that k concatenated with k+1 is a square.

183, 328, 528, 715, 6099, 13224, 40495, 106755, 453288, 2066115, 2975208, 22145328, 28027683, 110213248, 110667555, 147928995, 178838403, 226123528, 275074575, 333052608, 378698224, 445332888, 446245635

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Comments

Also called Sastry numbers. - Lekraj Beedassy, Jul 18 2008

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 183, p. 56, Ellipses, Paris 2008.

Links

• Giovanni Resta, Table of n, a(n) for n = 1..198 (terms < 10^20)

Crossrefs

Cf. A030466, A030467, A054214, A054215, A054216, A020339, A020340.

Programs

Mathematica

Select[{#,FromDigits[Join[IntegerDigits[#], IntegerDigits[1 + #]]]} & /@
  Flatten[Table[10*n + {0, 3, 4, 5, 8, 9}, {n, 10^5}]], IntegerQ[Sqrt[#[[2]]]] &] (* Hans Rudolf Widmer, Jun 30 2021 *)

PARI

isok(k) = issquare(eval(concat(Str(k), Str(k+1)))); \\ Michel Marcus, Jun 30 2021