A101954 - OEIS

%I #23 Jan 17 2019 13:44:06

%S 35,182,329,392,17519,27221

%N Indices of primes in sequence defined by A(0) = 27, A(n) = 10*A(n-1) - 53 for n > 0.

%C Numbers n such that (190*10^n + 53)/9 is prime.

%C Numbers n such that digit 2 followed by n >= 0 occurrences of digit 1 followed by digit 7 is prime.

%C Numbers corresponding to terms <= 392 are certified primes.

%C No further terms up to n=5000. [_Harvey P. Dale_, Aug 20 2011]

%C a(7) > 10^5. - Robert Price, Feb 07 2015

%D Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/2/21117.htm">Factorizations of 211...117</a>.

%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.

%F a(n) = A102949(n) - 1.

%e 2111111111111111111111111111111111117 is prime, hence 35 is a term.

%t a = 27; Flatten[Position[Table[a = 10*a - 53, {n, 500}], _?(PrimeQ[#] &)]]

%o (PARI) a=27;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-53)

%o (PARI) for(n=0,1500,if(isprime((190*10^n+53)/9),print1(n,",")))

%Y Cf. A000533, A002275, A102949.

%K nonn,hard,more

%O 1,1

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 23 2004

%E a(5)-a(6) derived from A102949 by _Robert Price_, Feb 07 2015