cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Original entry on oeis.org

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

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Author

Vladimir Shevelev, May 15 2010

Keywords

Comments

Records are in A177932, their positions in A177931.

Crossrefs

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

Programs

  • 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 *)

Formula

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

Extensions

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

A177932 Records in A177930.

Original entry on oeis.org

3, 5, 11, 29, 59, 137, 281, 569, 1151, 2309, 4649, 9341, 19139, 38711, 77489, 155381, 311681, 624047, 1248101, 2497421, 4998941, 10002437, 20005289, 40010609, 80021309, 160043909, 320090921, 640196267, 1280392739, 2560793201, 5121618767
Offset: 1

Views

Author

Vladimir Shevelev, May 15 2010

Keywords

Comments

By the construction of A177929, this is a subsequence of A001359.

Crossrefs

Cf. A177929 - A177931, A001359, A174514, A174216, A174217.

Formula

a(n) = A177930(A177931(n)) .

Extensions

Extended by R. J. Mathar, May 31 2010

A177943 Locations of records in A177942.

Original entry on oeis.org

1, 3, 4, 9, 11, 13, 20, 33, 42, 49, 84, 86, 107, 109, 123, 128, 191, 295, 296, 318, 330, 337, 396, 453, 481, 616, 663, 771, 882, 1105, 1180, 1257, 1431, 1659, 1856, 1936, 2130, 2370, 2584, 2651, 2790, 2959, 3009, 3080, 3121, 3189, 3503, 3639, 3879, 3902, 3961
Offset: 1

Views

Author

Vladimir Shevelev, May 15 2010

Keywords

Comments

Also: indices m for which A177941(m)-2 and A177941(m)+2 are cousin primes (A023200).

Crossrefs

Cf. A177941, A177942, A023200, A177929, A177930, A177931, A177945

Programs

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

Extensions

1 inserted, a(10) corrected and sequence extended by R. J. Mathar, Jun 30 2010
More terms from Michel Marcus, Dec 14 2018

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

Views

Author

Vladimir Shevelev, May 15 2010

Keywords

Comments

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

Crossrefs

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

Programs

  • 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

Extensions

Sequence extended by R. J. Mathar, Jun 30 2010
More terms from Michel Marcus, Dec 14 2018
Showing 1-4 of 4 results.

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