

A175075


Primes q with result 2 under iterations of {r mod (max prime p < r)} starting at r = q.


5



2, 5, 7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193, 199, 229, 241, 271, 283, 313, 349, 421, 433, 463, 523, 571, 601, 619, 643, 661, 811, 823, 829, 859, 883, 1021, 1033, 1051, 1063, 1093, 1153, 1231, 1279, 1291, 1303, 1321, 1429, 1453, 1483, 1489
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OFFSET

1,1


COMMENTS

a(1) = 2, a(n) = A006512(n1) 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, ...
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
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


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


FORMULA

A175072 \ A175076. [Anumber corrected by R. J. Mathar, Sep 25 2010]  Jaroslav Krizek, Jan 30 2010


EXAMPLE

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.


MATHEMATICA

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 *)


PROG

(PARI) is(n)=if(!isprime(n), return(0)); while(n>4, n=precprime(n1)); n==2 \\ Charles R Greathouse IV, Jan 12 2022
(PARI) has(n)=while(n>4, n=precprime(n1)); n==2
list(lim)=my(v=List([2]), p=3); forprime(q=5, lim, if(has(qp), listput(v, q)); p=q); Vec(v) \\ Charles R Greathouse IV, Jan 12 2022


CROSSREFS

Sequence in context: A069351 A275011 A094743 * A262392 A056985 A082182
Adjacent sequences: A175072 A175073 A175074 * A175076 A175077 A175078


KEYWORD

nonn


AUTHOR

Jaroslav Krizek, Jan 23 2010


EXTENSIONS

More terms from Robert G. Wilson v, Aug 09 2010
A175080 inserted in comment  R. J. Mathar, Sep 25 2010


STATUS

approved



