A177932 -id:A177932

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page 1

A177930

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

+10
6

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Records are in A177932, their positions in A177931.

LINKS

Table of n, a(n) for n=1..85.

FORMULA

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

MATHEMATICA

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 *)

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, May 15 2010

EXTENSIONS

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

STATUS

approved

A177945

Record values in A177942.

+10
2

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..34.

PROG

(PARI) 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

CROSSREFS

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