A090745 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.

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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..17.

Example

a(1) = 1 because 7 is prime and 7 has 1 digits.
a(2) = 2 because 97 is prime and 97 has 2 digits.
a(3) = 3 because 197 is prime and 197 has 3 digits.

Mathematica

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

Prog

(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);
for(j=0, 1000, if(isprime(test7(j)), print1(j+1, ", "))) \\ corrected by Michael S. Branicky and Michel Marcus, May 28 2023

Crossrefs

Cf. A090743, A090744, A090746.

Sequence in context: A144671 A073721 A285639 * A002229 A299158 A146747

Adjacent sequences: A090742 A090743 A090744 * A090746 A090747 A090748

Keyword

hard,nonn,base,more,less

Author

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

Extensions

Corrected and extended by Robert G. Wilson v, Feb 10 2004

Offset changed to 1 and a(14)-a(17) from Michael S. Branicky, May 28 2023

Status

approved