A052074 Squares of primes p^2 with the property that nextprime(p) is a substring of p^2.

529, 6889, 12769, 1261129, 40001200009, 107667328129, 145381301521, 510649971459777361, 24172491655282243145798689

Offset: 1

Author

Patrick De Geest, Jan 15 2000

Keywords

• nonn
• base
• more
• nice

Examples

			The corresponding primes p are 23, 83, 113, 1123, 200003, 328127, ..., the "next primes" are 29, 89, 127, 1129, 200009, 328129, ..., and these numbers are indeed substrings of 529, 6889, 12769, 1261129, 40001200009, 107667328129, ...
		

Crossrefs

Cf. A052073, A052075, A052076, A274932.

Programs

Mathematica

Select[Prime[Range[37*10^6]]^2,SequenceCount[IntegerDigits[#], IntegerDigits[ NextPrime[ Sqrt[#]]]]>0&] (* The program uses the SequenceCount function from Mathematica version 10 *) (* Harvey P. Dale, Jul 13 2016 *)

Extensions

a(8) from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 04 2006

Definition clarified and offset changed by N. J. A. Sloane, Jul 13 2016

a(9) from Giovanni Resta, May 24 2018