A090744 Consider numbers of the form ...53197531975319753, whose digits read from the right are 3,5,7,9,1,3,5,7,9,1,3,... Sequence gives lengths of these numbers that are primes.

1, 2, 5, 26, 1932, 13422, 16971

Offset

1,2

Comments

a(5) - Fermat and Lucas PRP! Tested with pfgw64 with switch -tc. - Marek Hubal, Mar 04 2019

a(6) - Fermat and Lucas PRP! Tested with pfgw64 with switch -tc. a(7) > 32000. - Marek Hubal, Mar 06 2019

Links

Table of n, a(n) for n=1..7.

Example

a(1)=1 because 3 is prime and 3 has 1 digit.
a(2)=2 because 53 is prime and 53 has 2 digits.
a(3)=5 because 19753 is prime and 19753 has 5 digits.

Mathematica

s = 0; Do[s = s + 10^n*Switch[ Mod[n, 5], 4, 1, 0, 3, 1, 5, 2, 7, 3, 9]; If[ PrimeQ[s], Print[n + 1]], {n, 0, 3000}] (* Robert G. Wilson v, Feb 19 2004 *)

Prog

(PARI) test3(n)= s=0; for(i=0, n, if(Mod(i, 5)==0, s=s+3*10^i, if(Mod(i, 5)==1, s=s+5*10^i, if(Mod(i, 5)==2, s=s+7*10^i, if(Mod(i, 5)==3, s=s+9*10^i, if(Mod(i, 5)==4, s=s+1*10^i, )))))); return(s);
for(j=0, 1000, if(isprime(test3(j)), print1(j+1, ", ")));

Crossrefs

Sequence in context: A023362 A138613 A299104 * A041571 A042259 A100105

Adjacent sequences: A090741 A090742 A090743 * A090745 A090746 A090747

Keyword

hard,nonn,base,more

Author

Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Feb 03 2004

Extensions

a(4) from Robert G. Wilson v, Feb 10 2004

a(5) from Marek Hubal, Mar 04 2019

a(6) from Marek Hubal, Mar 06 2019

Status

approved