

A090743


Consider numbers of the form ...31975319753197531, whose digits read from the right are 1,3,5,7,9,1,3,5,7,9,1,... Sequence gives lengths of these numbers which are primes.


2




OFFSET

1,1


COMMENTS

Approximately 1/3rd of numbers of the form described in the definition have a digit sum which is a multiple of 3 and therefore they are not prime numbers and do not have to be otherwise tested for prime status. The indices (i.e., integer lengths) of the first few such numbers are 3, 11, 12, 14, 15, 18, 26, 27, 29, 30, 33, 41, 42, 44, 45, 48, 56, 57, . . . Those indices appear to satisfy a linear recurrence having signature (1, 0, 0, 0, 1, 1) and can also be derived from the expansion of g.f. = (3+8*x+x^2+2*x^3+x^4)/((1+x)^2*(1+x+x^2+x^3+x^4)).  Harvey P. Dale, Dec 02 2018


LINKS



EXAMPLE

1 is not a prime; 31 is a 2digit prime, so 2 is a member.
531 is not prime, 7531 is not prime, 97531 is not prime, 197531 is not prime.
a(2)=58 because 5319753197531975319753197531975319753197531975319753197531 is prime and has 58 digits.


MATHEMATICA

s = 0; Do[s = s + 10^n*Switch[ Mod[n, 5], 0, 1, 1, 3, 2, 5, 3, 7, 4, 9]; If[ PrimeQ[s], Print[n + 1]], {n, 0, 2500}] (* Robert G. Wilson v, Feb 19 2004 *)
IntegerLength/@(Select[FromDigits/@Table[PadLeft[{}, n, {9, 7, 5, 3, 1}], {n, 100}], PrimeQ]) (* Harvey P. Dale, Nov 30 2018 *)


PROG

(PARI) test1(n)= s=0; for(i=0, n, \ if(Mod(i, 5)==0, s=s+1*10^i, \ if(Mod(i, 5)==1, s=s+3*10^i, \ if(Mod(i, 5)==2, s=s+5*10^i, \ if(Mod(i, 5)==3, s=s+7*10^i, \ if(Mod(i, 5)==4, s=s+9*10^i, \ )))))); return(s); for(j=0, 2000, if(isprime(test1(j)), print(j+1), print1(".")))


CROSSREFS



KEYWORD

hard,nonn,base


AUTHOR

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


EXTENSIONS



STATUS

approved



