A233358 Numbers n such that n^2 concatenated with n + 1 is prime.

2, 6, 30, 32, 38, 48, 50, 72, 90, 92, 98, 102, 110, 126, 128, 150, 182, 188, 212, 218, 230, 242, 258, 300, 318, 348, 398, 420, 440, 450, 462, 498, 516, 518, 530, 542, 572, 582, 636, 660, 662, 678, 702, 716, 726, 728, 746, 786, 798, 830, 848, 872, 878, 890, 908

Offset: 1

Author

K. D. Bajpai, Dec 07 2013

Keywords

• nonn
• base
• less

Comments

All the terms in sequence are even numbers, but none are congruent to 4 mod 10.

Examples

			6 is in the sequence because the concatenation of 6^2 and 6 + 1 gives 367, which is prime.
30 is in the sequence because the concatenation of 30^2 and 31 gives 90031, which is prime.
34 is not in the sequence because the concatenation of 34^2 and 35 gives 115635 = 3 * 5 * 13 * 593.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..5550

Crossrefs

Cf. A030465 (numbers n: concatenate n with n + 1 is prime).

Programs

Maple

KD := proc() local a,b; a:=parse(cat(n^2,n+1)); if  isprime(a) then RETURN (n); fi; end: seq(KD(), n=1..2000);