A102612 First nonzero terms in the sequences formed by the unique count of primes between an and (a+1)n.

22, 11, 18, 62, 59, 29, 12, 47, 106, 40, 17, 104, 94, 44, 83, 180, 22, 51, 65, 60, 177, 66, 189, 51, 175, 167, 112, 219, 204, 198, 193, 188, 36, 25, 281, 328, 267, 312, 305, 249, 244, 184, 175, 161

Offset: 1

Author

Cino Hilliard, Jan 30 2005

Keywords

• more
• nonn
• uned

Comments

Care should be taken to choose a sufficiently large n for a given m range for a in the script below. (50,1000) -> 22,11,18,62,59,29,12,47,106,40,17,104,94,44,83,22,.. (50,2000) -> 22,11,18,62,59,29,12,47,106,40,17,104,94,44,83,180,.. Notice the breakdown at the end. While the terms in the sequence tend to oscillate increasing, strange things are possible when more terms are listed. Conjecture: The number of terms in this sequence is infinite.

Examples

			S(1,2) = 22,36,47,79,98,114,134,173.. -> A084141 except for the first term
S(2,3) = 11,42,93,110,113,156,186..
S(3,4) = 18,100,102,147,200,203,238..
22,11,18 are the first 3 terms in the sequence.
		

Crossrefs

Cf. A084141.

Programs

PARI

betanap1n(m,n) = { local(a,c,c1,x,y); v=vector(10002); for(a=1,m, for(x=1,n, c=0; forprime(y=a*x+1,(a+1)*x-1, c++; ); v[x] = c; ); w=vecsort(v); for(x=1,10000, if(w[x]>0, if(w[x+1]<>w[x]&w[x+1]<>w[x+2], print1(w[x]+1",");break); ) ) ) }

Formula

S(a, b) = Sequence of the unique count of primes between an and bn n=1, 2, ...