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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 1-3 of 3 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

Views

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

A177931 Locations of records in A177930.

Original entry on oeis.org

1, 2, 4, 8, 10, 16, 20, 24, 29, 33, 36, 46, 76, 99, 108, 132, 179, 213, 217, 251, 286, 397, 431, 439, 445, 471, 535, 658, 677, 702, 780, 889, 1227, 1296, 1388, 1395, 1430, 1438, 1624, 1817, 2082, 2396, 2423, 2978, 3133, 3138, 3432, 3511, 3699, 3838, 4024, 4104, 4589, 4930
Offset: 1

Views

Author

Vladimir Shevelev, May 15 2010

Keywords

Comments

Or: positions m for which A177929(m)-1 and A177929(m)+1 are twin primes.

Crossrefs

Cf. A177929, A177930, A001359, A174514, A174216, A174217.

Programs

  • Maple
    A020639 := proc(n) numtheory[factorset](n) ; min(op(%)) ; end proc:
A177929 := proc(n) option remember; if n = 1 then 4; else d1 := A020639(procname(n-1)-1) ; d2 := A020639(procname(n-1)+1) ; procname(n-1)+min(d1,d2) -1; end if; end proc:
A177930 := proc(n) d1 := A020639(A177929(n)-1) ; d2 := A020639(A177929(n)+1) ; min(d1,d2) ; end proc:
read("transforms") ; L := [seq(A177930(n),n=1..1300)] ; RECORDS(L)[2] ; # R. J. Mathar, May 31 2010
  • 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];
Position[Table[b[n], {n, 1, 1000}], k_ /; PrimeQ[k-1] && PrimeQ[k+1]] // Flatten (* Jean-François Alcover, Feb 24 2024 *)

Extensions

Extended by R. J. Mathar, May 31 2010
More terms from Jean-François Alcover, Feb 24 2024

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
Showing 1-3 of 3 results.

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