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%I #18 Jan 20 2022 18:16:25
%S 2,5,7,13,19,31,43,61,73,103,109,139,151,181,193,199,229,241,271,283,
%T 313,349,421,433,463,523,571,601,619,643,661,811,823,829,859,883,1021,
%U 1033,1051,1063,1093,1153,1231,1279,1291,1303,1321,1429,1453,1483,1489
%N Primes q with result 2 under iterations of {r mod (max prime p < r)} starting at r = q.
%C a(1) = 2, a(n) = A006512(n-1) for 2 <= n <= 82, a(83) = 2999. Sequence is the union of A006512 and A175080. Subsequence of A175072. Primes q with some results of {2, 28, 36, 52, 58, 66, ... } under first step of iteration of {r mod (max prime p < r)} starting at r = q, i.e. number 2 and primes q such that difference q and previous prime is equal to some of the values 2, 28, 36, 52, 58, 66, ...
%C Not the same as A094743: contains 2999, 3299, 5147, 5981, 8999, 9587, 10037, 10427, 10559, 10937, 11579, 12889, ... that are absent from that sequence. Up to 10^9, there are 3247366 terms in this sequence that are not in A094743, though every term from that sequence appears here. Is A094743 a subsequence of this sequence? - _Charles R Greathouse IV_, Jan 12 2022
%C It suffices to stop after the iterations yield a number less than 5 and check if the result is 2. Under this procedure, 2 takes 0 iterations, 5 is the first prime to take 1 iteration, 29 is the first to take 2 iterations, 2999 is the first to take 3 iterations, and 401429925999155063 is the first to take 4 iterations. - _Charles R Greathouse IV_, Jan 14 2022
%H Charles R Greathouse IV, <a href="/A175075/b175075.txt">Table of n, a(n) for n = 1..10000</a>
%F A175072 \ A175076. [A-number corrected by _R. J. Mathar_, Sep 25 2010] - _Jaroslav Krizek_, Jan 30 2010
%e Iteration procedure for a(5) = 19: 19 mod 17 = 2. Iteration procedure for a(83) = 2999: 2999 mod 2971 = 28, 28 mod 23 = 5, 5 mod 3 = 2.
%t fQ[p_] := Block[{r = p}, While[r > 2, r = Mod[r, NextPrime[r, -1]]]; r == 2]; Select[ Prime@ Range@ 253, fQ] (* _Robert G. Wilson v_, Aug 09 2010 *)
%o (PARI) is(n)=if(!isprime(n), return(0)); while(n>4, n-=precprime(n-1)); n==2 \\ _Charles R Greathouse IV_, Jan 12 2022
%o (PARI) has(n)=while(n>4, n-=precprime(n-1)); n==2
%o list(lim)=my(v=List([2]),p=3); forprime(q=5,lim, if(has(q-p), listput(v,q)); p=q); Vec(v) \\ _Charles R Greathouse IV_, Jan 12 2022
%K nonn
%O 1,1
%A _Jaroslav Krizek_, Jan 23 2010
%E More terms from _Robert G. Wilson v_, Aug 09 2010
%E A175080 inserted in comment - _R. J. Mathar_, Sep 25 2010
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