A175075 Primes q with result 2 under iterations of {r mod (max prime p < r)} starting at r = q.

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

Offset: 1

Author

Jaroslav Krizek, Jan 23 2010

Keywords

• nonn

Comments

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, ...

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

Examples

			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.
		

Links

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

Programs

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 *)

PARI

is(n)=if(!isprime(n), return(0)); while(n>4, n-=precprime(n-1)); n==2 \\ Charles R Greathouse IV, Jan 12 2022

PARI

has(n)=while(n>4, n-=precprime(n-1)); n==2
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

Formula

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

Extensions

More terms from Robert G. Wilson v, Aug 09 2010

A175080 inserted in comment - R. J. Mathar, Sep 25 2010