A028868 Primes that when squared give numbers with digits in nonascending order.

2, 3, 29, 31

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base
• hard
• more

Comments

No other solutions below 2*10^9 (probably finite). - Dec 15 1999

No other solutions below 10^20. - David A. Corneth, Oct 28 2023, recomputed after a remark from Max Alekseyev, David A. Corneth, Aug 20 2024

Primes p such that p^2 is in A062826. - Max Alekseyev, Aug 18 2024

Examples

			From _David A. Corneth_, Oct 28 2023: (Start)
31 is in the sequence as 31 is prime and 31^2 = 961 which has its digits in nonascending order.
2979 is not in the sequence even though 2979^2 = 8874441 does have digits in nonascending order but 2979 = 3^2 * 331 is not prime. (End)
		

Links

• David A. Corneth, PARI program

Crossrefs

Cf. A028869, A028865, A028866, A062826.

Programs

PARI

is(n) = my(d = digits(n^2)); d == vecsort(d,,4) && isprime(n) \\ David A. Corneth, Oct 28 2023

PARI

\\ see link for a faster program

Extensions

Name clarified by Jon E. Schoenfield, Oct 27 2023