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 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
 2, 58, 64, 81, 5671, 7234, 18999 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS No further terms below 5456. - Robert G. Wilson v, Feb 18 2004 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 Table of n, a(n) for n=1..7. EXAMPLE 1 is not a prime; 31 is a 2-digit 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 Cf. A090744, A090745, A090746. Sequence in context: A024237 A030263 A359242 * A104494 A121931 A343578 Adjacent sequences: A090740 A090741 A090742 * A090744 A090745 A090746 KEYWORD hard,nonn,base AUTHOR mohammed bouayoun (bouyao(AT)wanadoo.fr), Feb 03 2004 EXTENSIONS a(5)-a(7) from Michael S. Branicky, May 27 2023 STATUS approved

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Last modified December 5 00:18 EST 2023. Contains 367565 sequences. (Running on oeis4.)