A090871 - OEIS

%I #14 Mar 22 2023 08:43:25

%S 589407,2372675,5609052,5698663,12353466,12534100,14155932,24208353,

%T 25303609,30939821,32915465,36240880,37168122,50679993,52677223,

%U 60090497,66071478,67690661,75747212,88096704,89077730,98871534,115631955,119515953,127817446,134262693

%N Numbers k such that the six numbers 1.prime(k).prime(k+1), prime(k).1.prime(k+1), prime(k).prime(k+1).1, 1.prime(k-1).prime(k), prime(k-1).1.prime(k) and prime(k-1).prime(k).1, where "." denotes concatenation, are primes.

%e 5698663 is a term because prime(5698662)=98842171, prime(5698663)=98842223 and prime(5698664)=98842231 and the six numbers 19884217198842223, 98842171198842223, 98842171988422231, 19884222398842231, 98842223198842231 and 98842223988422311 are primes.

%t v={}; Do[If[PrimeQ[FromDigits[Join[{1}, IntegerDigits[Prime[k-1]], IntegerDigits [Prime[k]]]]]&&PrimeQ[FromDigits[Join[IntegerDigits[Prime[k-1]], {1}, IntegerDigits[Prime[k]]]]]&&PrimeQ[FromDigits[Join[IntegerDigits [Prime[k-1]], IntegerDigits[Prime[k]], {1}]]]&& PrimeQ[FromDigits [Join[{1}, IntegerDigits[Prime[k]], IntegerDigits[Prime[k+1]]]]] &&PrimeQ[FromDigits[Join[IntegerDigits[Prime[k]], {1}, IntegerDigits[ Prime[k+1]]]]]&& PrimeQ[FromDigits[Join[IntegerDigits[Prime[k]], IntegerDigits[Prime[k+1]], {1}]]], v=Append[v, k]; Print[v]], {k, 2, 3*10^7}]; v

%K nonn,base

%O 1,1

%A _Farideh Firoozbakht_, Jan 25 2004

%E a(9) and beyond from _Michael S. Branicky_, Mar 21 2023