A103791
Index of the first occurrence of A019565(2n-1) in sequence A103790.
Original entry on oeis.org
2, 4, 8, 29, 24, 78, 65, 90, 449, 280, 400, 124, 935, 589, 1743, 325, 2001, 2863, 3150, 2026, 5680, 5156, 4016, 10403, 22626, 2358, 19242, 14356, 19543, 7666, 20555, 29104, 64045, 56438, 84993, 15346, 37400, 13663, 83487, 58651, 162225, 111880
Offset: 1
A103790(2)=1*2*1-1; => a(1)=2
A103790(4)=3*2*2-1; => a(2)=4
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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 < 69, 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]]]
A103792
Index k of the first occurrence of A019565(2n-1) as the smallest term that makes prime(k)-A019565(2n-1) prime.
Original entry on oeis.org
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
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.
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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]]]
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