A124136 a(n) is the smallest prime when larger number of primes arise between numbers and their doubles. Note for example that there are 8 primes between 34 and 2*34=68 and 35 and 2*35=70, but 34 and 35 are not primes and a(8)=37, which is the smallest prime where there are already nine primes between numbers 36, 37, 38, 39, 41, 43, 44, 47, 48 and their doubles.

2, 7, 11, 17, 23, 29, 31, 37, 53, 59, 71, 79, 89, 97, 101, 127, 137, 149, 157, 179, 191, 211, 223, 233, 251, 257, 263, 293, 307, 311, 331, 347, 367, 373, 379, 389, 409, 419, 431, 443, 457, 479, 487, 499, 521, 541, 547, 557, 563, 587, 599, 613, 617, 631, 641

Offset

1,1

Comments

a(n) is the index of first occurrence of prime n in A060715.

Links

Table of n, a(n) for n=1..55.

Example

a(2)=7 since 7 is first prime when two primes are between 7 and its double.
a(10)=59 since 59 is first prime after 55 and 56 when ten primes are between these numbers and their doubles.

Maple

ts_c:=proc(n) local i, j, st_p, max_stp, ans; ans:= [ ]: st_p:=0: max_stp:=0: for i from 2 to n do for j from i+1 to 2*i-1 do if (isprime(j) = 'true') then st_p:=st_p+1: fi od: if (st_p > max_stp and isprime(i) = 'true') then max_stp := st_p: ans:=[ op(ans), i ]: fi; st_p:=0: od: RETURN(ans) end: ts_c(1200);

Crossrefs

Cf. A060756, A060715, A084139.

Sequence in context: A168421 A038942 A175283 * A156828 A019385 A075552

Adjacent sequences: A124133 A124134 A124135 * A124137 A124138 A124139

Keyword

nonn,uned

Author

Jani Melik, Nov 30 2006

Status

approved