A030470 Numbers k such that k concatenated with k+1, k+2, k+3 is prime.

4, 14, 20, 34, 58, 64, 118, 140, 148, 176, 196, 218, 220, 236, 238, 268, 278, 286, 316, 334, 374, 386, 398, 428, 430, 436, 446, 460, 470, 496, 508, 514, 550, 566, 568, 590, 610, 616, 634, 644, 670, 674, 688, 706, 718, 728, 740, 746, 764, 770

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Comments

All terms must be even; otherwise k+3 would be an even number and thus the concatenation of k, k+1, k+2, and k+3 would not be prime. - Harvey P. Dale, Jul 05 2021

Examples

			4567 is prime, so 4 is a term.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Maple

dcat:= proc(x,y) 10^(1+ilog10(y))*x+y end proc:
filter:= proc(n) isprime(dcat(n,dcat(n+1,dcat(n+2,n+3)))) end proc:
select(filter, [seq(i,i=2..1000,2)]); # Robert Israel, Apr 01 2021

Mathematica

Select[2*Range[400],PrimeQ[FromDigits[Flatten[IntegerDigits/@(Range[ 0,3]+#)]]]&] (* Harvey P. Dale, Jul 05 2021 *)

PARI

is(n)=isprime(eval(Str(n,n+1,n+2,n+3))) \\ Charles R Greathouse IV, Jun 12 2017