A239992 Primes formed by concatenating a square number S with S+1, where S+1 is a prime number.

3637, 576577, 2433624337, 3240032401, 4410044101, 6969669697, 352836352837, 404496404497, 746496746497, 16641001664101, 17424001742401, 20050562005057, 20736002073601, 24523562452357, 26049962604997, 28022762802277, 34596003459601, 35494563549457, 42600964260097

Offset: 1

Author

K. D. Bajpai, Mar 30 2014

Keywords

• nonn
• base

Comments

It is observed that each term in the sequence ends either with digit 1 or 7.

Examples

			3637 is a prime formed by concatenaing 36 with 37 where 36= 6^2 and (36+1)= 37 is a prime.
576577 is a prime formed by concatenaing 576 with 577 where 576= 24^2 and (576+1)= 577 is a prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..1060

Crossrefs

Cf. A000040, A030458.

Programs

Maple

with(StringTools):KD := proc() local a,b,s;s:=n*n;b:=s+1; if isprime(b) then a:= parse(cat(s,b )); if isprime(a) then RETURN (a); fi; fi;end: seq(KD(), n=1..5000);