A090745 - OEIS

%I #35 Aug 04 2024 01:30:55

%S 1,2,3,5,6,7,16,17,18,104,127,213,1143,4654,4897,17046,33424,47407

%N Consider numbers of the form ...7531975319753197, whose digits read from the right are 7,9,1,3,5,7,9,1,3,5,7,... Sequence gives lengths of these numbers that are primes.

%C Numbers n such that 53197 * (10^(5*m)-1)/99999 + (53197 mod 10^(n mod 5))*10^(5*m) is prime, where m = floor(n/5). - _Max Alekseyev_, Nov 11 2012

%e a(1) = 1 because 7 is prime and 7 has 1 digits.

%e a(2) = 2 because 97 is prime and 97 has 2 digits.

%e a(3) = 3 because 197 is prime and 197 has 3 digits.

%t s = 0; Do[s = s + 10^n*Switch[ Mod[n, 5], 2, 1, 3, 3, 4, 5, 0, 7, 1, 9]; If[ PrimeQ[s], Print[n + 1]], {n, 0, 3000}] (* _Robert G. Wilson v_, Feb 10 2004 *)

%t Position[Table[FromDigits[PadLeft[{},n,{5,3,1,9,7}]],{n,1200}],_?PrimeQ]// Flatten (* _Harvey P. Dale_, Mar 30 2019 *)

%o (PARI) test7(n)= s=0; for(i=0, n, if(Mod(i, 5)==0, s=s+7*10^i, if(Mod(i, 5)==1, s=s+9*10^i, if(Mod(i, 5)==2, s=s+1*10^i, if(Mod(i, 5)==3, s=s+3*10^i, if(Mod(i, 5)==4, s=s+5*10^i, )))))); return(s);

%o for(j=0,1000,if(isprime(test7(j)),print1(j+1, ", "))) \\ corrected by _Michael S. Branicky_ and _Michel Marcus_, May 28 2023

%Y Cf. A090743, A090744, A090746.

%K hard,nonn,base,more,less

%O 1,2

%A mohammed bouayoun (bouyao(AT)wanadoo.fr), Feb 03 2004

%E Corrected and extended by _Robert G. Wilson v_, Feb 10 2004

%E Offset changed to 1 and a(14)-a(17) from _Michael S. Branicky_, May 28 2023

%E a(18) from _Michael S. Branicky_, Aug 03 2024