A177932 -id:A177932 - cp's OEIS frontend

A177930 a(n) is the smallest prime divisor of (A177929(n)-1)*(A177929(n)+1).

3, 5, 3, 11, 3, 5, 3, 29, 3, 59, 3, 7, 5, 3, 7, 137, 3, 5, 3, 281, 3, 5, 3, 569, 3, 7, 5, 3, 1151, 3, 5, 3, 2309, 3, 31, 4649, 3, 17, 3, 7, 5, 3, 7, 5, 3, 9341, 3, 5, 3, 11, 3, 59, 3, 29, 3, 19, 7, 5, 3, 7, 19, 5, 3, 7, 109, 5, 3, 61, 7, 79, 5, 3, 13, 5, 3, 19139, 3, 101, 3, 7, 13, 11, 3, 71, 3

Offset: 1

Vladimir Shevelev, May 15 2010

nonn

Records are in A177932, their positions in A177931.

Cf. A001359, A020639, A177929, A174514, A174216, A174217

lpf[n_] := FactorInteger[n][[1, 1]];
b[n_] := b[n] = If[n == 1, 4, b[n-1]+lpf[b[n-1]^2-1]-1];
a[n_] := lpf[b[n]^2-1];
Table[a[n], {n, 1, 85}] (* Jean-François Alcover, May 13 2023 *)

a(n) = A020639( (A177929(n))^2 -1 ).

A 7 replaced by 17 and sequence extended by R. J. Mathar, May 31 2010

A177945 Record values in A177942.

Original entry on oeis.org

3, 7, 13, 37, 79, 163, 349, 757, 1567, 3163, 6547, 13099, 26497, 52999, 106273, 212557, 426889, 855427, 1710853, 3421903, 6845869, 13691767, 27385087, 54771007, 109542907, 219096259, 438203677, 876417229, 1752875893, 3505814527, 7011656629, 14023322167, 28046754727, 56093637367

Offset: 1

Vladimir Shevelev, May 15 2010

nonn

From the construction of A177941, this is a subsequence of A023200.

Cf. A177941, A177942, A177943, A023200, A177929, A177930, A177931, A177932.

listar(nn) = {my(va = vector(nn), rec = 0); va[1] = 5; for (n=2, nn, p = factor(va[n-1]^2-4)[1,1]; if (p > rec, print1(p, ", "); rec = p); va[n] = va[n-1] + p - 1;);} \\ Michel Marcus, Dec 14 2018

Sequence extended by R. J. Mathar, Jun 30 2010

More terms from Michel Marcus, Dec 14 2018

cp's OEIS Frontend

A177930 a(n) is the smallest prime divisor of (A177929(n)-1)*(A177929(n)+1).

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