A103792 Index k of the first occurrence of A019565(2n-1) as the smallest term that makes prime(k)-A019565(2n-1) prime.

3, 5, 13, 25, 67, 79, 140, 127, 345, 129, 222, 206, 479, 1008, 1577, 766, 2583, 869, 1406, 3427, 5367, 4215, 4141, 9716, 23067, 5030, 13586, 7502, 17340, 19211, 14991, 30961, 27008, 82915, 84387, 91387, 92294, 32886, 30890, 70886, 271430, 131908

Offset

1,1

Links

Table of n, a(n) for n=1..42.

Example

n=1: A019565(2n-1)=2; Prime(3)-2=3 is prime, so a(1)=3;
Prime(4)-A019565(1)=5 is prime, not counted;
n=2: A019565(2n-1)=6; Prime(5)-A019565(1)=9 is not prime; ... Prime(5)-6=5 is prime, so a(2)=5;
Prime(6)-A019565(1)=11 is prime, not counted;
...
Prime(12)-A019565(3)=31 is prime, not counted;
n=3; A019565(2n-1)=10; Prime(13)-2=39, Prime(13)-6=35; Prime(13)-10=31 is prime, so a(3)=13.

Mathematica

A019565 = Function[tn, k1 = tn; o = 1; tt = 1; While[k1 > 0, k2 = Mod[k1, 2]; If[k2 == 1, tt = tt*Prime[o]]; k1 = (k1 - k2)/2; o = o + 1]; tt]; Array[fa, {1, 500}]; Do[fa[n] = 0, {n, 1, 500}]; n = 2; npd = Prime[n]; ct = 1; wt = 1; While[wt < 200, cr = (ct + 1)/2; If[fa[cr] == 0, fa[cr] = n; While[fa[wt] > 0, Print[fa[wt]]; wt = wt + 1]]; n = n + 1; npd = Prime[n]; ct = 1; tt = ct; cp = npd - A019565[tt]; While[ ! (PrimeQ[cp]), ct = ct + 1; tt = ct; cp = npd - A019565[tt]]]

Crossrefs

Cf. A103790, A103791.

Sequence in context: A098615 A026720 A026003 * A076156 A339984 A141630

Adjacent sequences: A103789 A103790 A103791 * A103793 A103794 A103795

Keyword

hard,nonn

Author

Lei Zhou, Feb 28 2005

Status

approved