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.

0, 0, 48, 300, 111, 234, 1395, 546, 2526, 5742, 753, 12369, 5658, 94572, 6744, 134649, 32523, 43071, 213927, 256116, 8172, 431904, 57138, 433125, 123225, 711447, 318501, 40758, 150063, 184602, 134661, 377778, 129048, 504678, 88113, 3174738

Offset: 1

Author

Farideh Firoozbakht, Aug 18 2004

Keywords

• base
• nonn

Comments

a(50)= 10718757, can you find a(100)?

Examples

			a(4)=300 because 10(10^3+300)+ 1, 10(10^3+300)+ 3, 10(10^3+300)+ 7 and 10(10^3+300)+1, are primes and 300 is the smallest number with this property.
		

Crossrefs

Cf. A011557, A097638, A007811.

Programs

Mathematica

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}]
Table[Module[{m=0,s=10^n},While[AnyTrue[10(s+m)+{1,3,7,9},CompositeQ],m++];m],{n,0,35}] (* Harvey P. Dale, Sep 19 2022 *)

PARI

isok(m, n) = my(s=10^(n-1)+ m); ispseudoprime(10*s+1) && ispseudoprime(10*s+3) && ispseudoprime(10*s+7) && ispseudoprime(10*s+9);
a(n) = my(m=0); while (!isok(m, n), m++); m; \\ Michel Marcus, Aug 09 2023

Formula

a(n) = A097638(n) - 10^(n-1).