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Sastry numbers
A number  $n$  is a Sastry number if concatenated with  $n+1$  it gives a square.

For example, 183 is a Sastry number because 183184 is the square of 428.

F.Luca has proved that there exists a Sastry number with  $k$  digits if and only if  $10^k+1$  is not a prime number, a thing that happen only for  $k=1$  and  $k=2$  for  $k<10^5$.

The first Sastry numbers are 183, 328, 528, 715, 6099, 13224, 40495, 106755, 453288, 2066115, 2975208, 22145328, 28027683 more terms

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here
remainders of Sastry numbers

A graph displaying how many Sastry numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.
divisibility of Sastry numbers
Useful links OEIS, Sequence A030465
Sastry numbers can also be... (you may click on names or numbers and on + to get more values)

aban 183 328 528 715 abundant 528 13224 453288 2975208 22145328 alternating 183 amenable 328 528 13224 453288 2975208 22145328 110213248 226123528 333052608 378698224 + 734693880 801777640 826446280 897506928 apocalyptic 528 6099 13224 arithmetic 183 715 6099 13224 40495 106755 453288 2066115 2975208 binomial 528 715 congruent 183 40495 Cunningham 528 13224 cyclic 40495 D-number 183 deficient 183 328 715 6099 40495 106755 2066115 dig.balanced 528 13224 147928995 178838403 Duffinian 183 715 economical 183 emirpimes 183 equidigital 183 evil 183 528 715 40495 106755 453288 2066115 2975208 28027683 110213248 + 657515568 734693880 898802499 924910143 fibodiv 183 gapful 106755 110667555 147928995 275074575 1568473680 13973312520 27221172024 30449526120 35535821475 85677207840 happy 2066115 Harshad 715 13224 647238399 657515568 801777640 826446280 1568473680 hoax 22145328 Hogben 183 inconsummate 106755 interprime 13224 junction 715 2066115 lucky 106755 modest 6099 nude 13224 oban 328 528 715 odious 328 6099 13224 22145328 110667555 226123528 275074575 378698224 445332888 446245635 + 574930563 801777640 826446280 897506928 pentagonal 715 pernicious 328 528 13224 practical 528 13224 453288 2975208 pseudoperfect 528 13224 453288 repunit 183 40495 Ruth-Aaron 715 self 226123528 semiprime 183 sphenic 715 6099 super-d 715 106755 tau 328 110213248 333052608 triangular 528 Ulam 2975208 unprimeable 328 untouchable 13224 wasteful 328 528 715 6099 13224 40495 106755 453288 2066115 2975208 Zumkeller 528 13224