A179234 a(n) is the smallest prime q such that, for the previous prime p and the following prime r, the fraction (r-q)/(q-p) has denominator n in lowest terms.
3, 11, 29, 367, 149, 521, 127, 1847, 1087, 1657, 1151, 4201, 2503, 2999, 5779, 10831, 1361, 9587, 30631, 19373, 16183, 36433, 81509, 28277, 31957, 25523, 40343, 82129, 44351, 102761, 34123, 89753, 282559, 134581, 173429, 705389, 404671, 212777, 371027, 1060861, 265703, 461801, 156007, 544367, 576881, 927961, 1101071, 1904407, 604171, 396833
Offset: 1
Keywords
Examples
For q=3 we have (r-q)/(q-p)=2/1. Therefore, a(1)=3. For q=5: (r-q)/(q-p) = 1/1; for q = 7: (r-q)/(q-p) = 2/1; for q = 11: (r-q)/(q-p) = 1/2. Therefore, a(2)=11.
Links
- Robert G. Wilson v, Table of n, a(n) for n = 1..123
Programs
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Mathematica
f[n_] := Block[{p = 2, q = 3, r = 5}, While[ Denominator[(r - q)/(q - p)] != n, p = q; q = r; r = NextPrime@ r]; q]; Array[f, 50] p = 2; q = 3; r = 5; t[] = 0; While[q < 100000000, If[ t[ Denominator[(r - q)/(q - p)]] == 0, t[ Denominator[(r - q)/(q - p)]] = q]; p = q; q = r; r = NextPrime@ r]; t@# & /@ Range@100 (* _Robert G. Wilson v, Dec 11 2016 *) -
PARI
a(n)=my(p=2,q=3);forprime(r=5,default(primelimit),if(denominator((r-q)/(q-p))==n,return(q));p=q;q=r)
Extensions
Revised definition, new program, and terms past a(5) from Charles R Greathouse IV, Jan 12 2011
Comments