

A321151


Primes that yield squares after deletion of their zero digits.


1



409, 1021, 1069, 1201, 1609, 2089, 3061, 5209, 9601, 10069, 10369, 18049, 20089, 20809, 37021, 37201, 40009, 44089, 44809, 50329, 50929, 52009, 59029, 59209, 60889, 62401, 70921, 79201, 96001, 100069, 100609, 101449, 102001, 102769, 103069, 104161, 106129, 106801, 108769, 109321
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OFFSET

1,1


COMMENTS

Subsequence of A056709. The squares divisible by 2, 3 or 5 cannot be obtained. Most of the squares obtained seem to be squares of prime or semiprime numbers. Among the first 399 squares obtained are 289 squares of prime numbers, 104 squares of semiprimes and 6 other squares; these squares were obtained by testing the prime numbers up to 10^7. Deletion of the zero digits from primes up to 10^8 yields 929 squares of prime numbers, 506 squares of semiprimes and 47 other squares. Do similar results occur when larger primes are considered?
From David A. Corneth, Nov 26 2018: (Start)
Terms can be obtained by listing squares coprime to 30, inserting zeros between digits, and testing the primality of the resulting numbers.
Records for omega(s) where s is a square producing a term occur at terms 409, 50929, 10713481, 3601722361, 1531869148081, 807916258118689. (End)


LINKS

David A. Corneth, Table of n, a(n) for n = 1..17124 (terms < 10^10)
David A. Corneth, PARI program


EXAMPLE

409 is prime and 49 = 7^2 is a square.
9601 is prime and 961 = 31^2 is a square.
20809 is prime and 289 = 17^2 is a square.
10069 is prime and 169 = 13^2 is a square.
103069 is prime and 1369 = 37^2 is a square.
1030069 is prime and 1369 = 37^2 is a square.


MATHEMATICA

aQ[n_] := PrimeQ[n] && IntegerQ[Sqrt[FromDigits[Select[IntegerDigits[n], #!=0 &]]]]; Select[Range[100000], aQ] (* Amiram Eldar, Nov 25 2018 *)


PROG

(PARI) isok(p) = isprime(p) && issquare(fromdigits(select(x>x, digits(p)))); \\ Michel Marcus, Nov 26 2018
(PARI) \\ See Corneth link \\ David A. Corneth, Nov 26 2018


CROSSREFS

Cf. A000040, A000290, A052041, A056709, A256186.
Sequence in context: A052354 A213079 A260173 * A052376 A201483 A031601
Adjacent sequences: A321148 A321149 A321150 * A321152 A321153 A321154


KEYWORD

nonn,base


AUTHOR

Marius A. Burtea, Nov 23 2018


STATUS

approved



