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Numbers n such that 1 + 46* Sum_{k=1..n} 100^(k-1) is prime.
1

%I #68 Jul 09 2023 12:19:33

%S 1,3,4,6,9,45,57,130,142,198,273,331,2494,8437,10210,17377,19972

%N Numbers n such that 1 + 46* Sum_{k=1..n} 100^(k-1) is prime.

%C Equivalently n is the number of As in a prime P of the form AAA...AA+1 where A=46. n is also equal to half the number of digits in P. The first 11 numbers of the sequence are validated by D. Alpern's java applet (see link).

%C Equivalently primes of the form (100^n - 1) * 46/99 + 1. - _Charles R Greathouse IV_, Jan 22 2015

%C a(12) proved prime with Primo 3.0.7. - _Charles R Greathouse IV_, Jan 22 2015

%H Dario A. Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>.

%e 47 is prime, so 1 is in the sequence.

%e 4647 is not prime, so 2 is not in the sequence.

%e 464647 is prime, so 3 is in the sequence.

%e 46464647 is prime, so 4 is in the sequence.

%o (PARI) isok(n) = isprime(1 + 46*sum(k=1, n, 100^(k-1))); \\ _Michel Marcus_, Jan 22 2015

%o (PARI) is(n)=ispseudoprime(46*(100^n-1)/99+1) \\ _Charles R Greathouse IV_, Jan 22 2015

%o (PFGW) ABC2 46*(100^$a-1)/99+1

%o a: from 1 to 10000

%o _Charles R Greathouse IV_, Jan 22 2015

%Y Cf. A110705.

%K nonn,base,more

%O 1,2

%A _Mohsen Hozan_, Jan 21 2015

%E a(13)-a(14) from _Charles R Greathouse IV_, Jan 22 2015

%E a(15) from _Charles R Greathouse IV_, Jan 23 2015

%E a(16)-a(17) from _Charles R Greathouse IV_, Jan 26 2015