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A097639 a(n) is the smallest number m such that for the n-digit number s=10^(n-1)+ m, 10*s+1, 10*s+3, 10*s+7 and 10*s+9 are primes. 1

%I

%S 0,0,48,300,111,234,1395,546,2526,5742,753,12369,5658,94572,6744,

%T 134649,32523,43071,213927,256116,8172,431904,57138,433125,123225,

%U 711447,318501,40758,150063,184602,134661,377778,129048,504678,88113,3174738

%N a(n) is the smallest number m such that for the n-digit number s=10^(n-1)+ m, 10*s+1, 10*s+3, 10*s+7 and 10*s+9 are primes.

%C a(n)=A097638(n)-10^(n-1). a(50)= 10718757, can you find a(100)?

%F a[n_]:=(For[m=0, !(PrimeQ[10^n+10m+1]&&PrimeQ[10^n+10m+3]&&PrimeQ [10^n+10m+7]&&PrimeQ[10^n+10m+9]), m++ ];m);

%e a(4)=300 because 10(10^3+300)+ 1, 10(10^3+300)+ 3,10(10^3+300)+ 7 &

%e 10(10^3+300)+1, are primes and 300 is the smallest number with

%e this property.

%t a[n_]:=(For[m=0, !(PrimeQ[10^n+10m+1]&&PrimeQ[10^n+10m+3]&&PrimeQ[ 10^n+10m+7]&&PrimeQ[10^n+10m+9]), m++ ];m);Table[a[n], {n, 43}]

%Y Cf. A097638, A007811.

%K base,nonn

%O 1,3

%A _Farideh Firoozbakht_, Aug 18 2004

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Last modified October 25 03:28 EDT 2021. Contains 348237 sequences. (Running on oeis4.)