A100997 - OEIS

%I #23 Dec 14 2025 11:49:35

%S 2,3,4,8,21,26,35,56,61,77,200,536,695,789,904,1037,66885,70499,91835,

%T 100612,127239,380733,583695,719054,823036,862867

%N Indices of primes in sequence defined by A(0) = 91, A(m) = 10*A(m-1) - 9 for m > 0.

%C Numbers k such that 90*10^k + 1 is prime.

%C Numbers k such that digit 9 followed by k >= 0 occurrences of digit 0 followed by digit 1 is prime.

%C Numbers corresponding to terms <= 1037 are certified primes.

%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/9/90001.htm#prime">Prime numbers of the form 900...001</a>.

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

%F a(n) = A056797(n) - 1.

%e 900001 is prime, hence 4 is a term.

%o (PARI) a=91;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-9)

%o (PARI) for(n=0,1500,if(isprime(90*10^n+1),print1(n,",")))

%Y Cf. A000533, A002275, A056797.

%K nonn,hard,more

%O 1,1

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 26 2004

%E a(17) from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

%E a(18)-a(21) from Kamada data by _Ray Chandler_, Apr 28 2015

%E a(22)-a(23) from Kamada data by _Mohammed Yaseen_, Jul 20 2021

%E a(24)-a(26) derived from A056797 by _Elmo R. Oliveira_, Dec 14 2025