OFFSET
1,1
COMMENTS
Also called Sastry numbers. - Lekraj Beedassy, Jul 18 2008
From Amiram Eldar, Feb 01 2026: (Start)
Named after the Indian mathematician and educator K. R. S. (Shankaranarayana) Sastry.
Luca (1997) proved that there exist a term with k digits if and only if 10^k + 1 is composite. (End)
REFERENCES
Jean-Marie De Koninck, Ces nombres qui nous fascinent, Entry 183, p. 56, Ellipses, Paris, 2008.
Florian Luca, On a problem of K. R. S. Sastry, Mathematics and Computer Education, Vol. 35, No. 2 (2001), pp. 125-135.
K. R. S. Sastry, Problem, Mathematics and Computer Education, Vol. 30, No. 1 (1997), p. 9.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..198 (terms < 10^20)
Nina Blokland, Perfect squares as a result of concatenating consecutive integers, Bachelor Thesis, Utrecht University, 2022.
Shyam Sunder Gupta, Elegance of Squares, Cubes, and Higher Powers, Exploring the Beauty of Fascinating Numbers, Springer, 2025. See Section 2.5.6, pp. 46-47.
Florian Luca and Pantelimon Stănică, Perfect Squares as the Concatenation of Consecutive Integers, American Mathematical Monthly, Vol. 121, No. 1 (2018), pp. 728-734.
Giovanni Resta, Sastry numbers, Numbersaplenty.
Gérard Villemin, Nombres successifs concaténés, Nombres de Sastry, NOMBRES - Curiosités, Théorie et Usages.
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 *)
PROG
(PARI) isok(k) = issquare(eval(concat(Str(k), Str(k+1)))); \\ Michel Marcus, Jun 30 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
a(24) onwards from Giovanni Resta, Oct 24 2013
STATUS
approved
