A090871 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.

589407, 2372675, 5609052, 5698663, 12353466, 12534100, 14155932, 24208353, 25303609, 30939821, 32915465, 36240880, 37168122, 50679993, 52677223, 60090497, 66071478, 67690661, 75747212, 88096704, 89077730, 98871534, 115631955, 119515953, 127817446, 134262693

Offset

1,1

Links

Table of n, a(n) for n=1..26.

Example

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.

Mathematica

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

Crossrefs

Sequence in context: A206222 A202160 A216927 * A237493 A232361 A236736

Adjacent sequences: A090868 A090869 A090870 * A090872 A090873 A090874

Keyword

nonn,base

Author

Farideh Firoozbakht, Jan 25 2004

Extensions

a(9) and beyond from Michael S. Branicky, Mar 21 2023

Status

approved