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.

A077322 Initial terms of rows of A077321.

Original entry on oeis.org

2, 3, 7, 17, 11, 43, 113, 89, 109, 131, 23, 157, 53, 449, 571, 593, 647, 487, 761, 821, 1303, 1013, 47, 1033, 1451, 1613, 2539, 1373, 59, 1831, 2543, 1889, 3499, 3299, 2591, 2557, 149, 4637, 6163, 3761, 83, 4243, 173, 3917, 6571, 5843, 283, 4273, 5783, 6551
Offset: 1

Views

Author

Amarnath Murthy, Nov 04 2002

Keywords

Crossrefs

Cf. A077321, A077323, A077324, A077325.

Programs

  • Maple
    A077322 := proc(nmax) local n,a,T,i,p ; T := [] ; a := [] ; n :=1 ; while nops(a) < nmax do for i from 1 to n do p := 2 ; while ( p in T ) or (p-1) mod n <> 0 do p := nextprime(p) ; od ; T := [op(T),p] ; if i = 1 then a := [op(a),p] ; fi ; od ; n := n+1 ; od ; RETURN(a) ; end: A077322(50) ; # R. J. Mathar, Feb 03 2007
  • Mathematica
    nrows = 50;
A077321[nmax_] := Module[{n = 1, a = {}, i, p}, While[ Length[a] < nmax, For[i = 1, i <= n, i++, p = 2; While[MemberQ[a, p] || Mod[p - 1, n] != 0, p = NextPrime[p]]; a = Append[a, p]]; n = n + 1]; Return[a]];
T = A077321[nmax = (nrows^2 - nrows + 2)/2];
a[n_] := T[[(n^2 - n + 2)/2]];
Table[a[n], {n, 1, nrows}] (* Jean-François Alcover, May 30 2023, after R. J. Mathar *)

Extensions

More terms from R. J. Mathar, Feb 03 2007

A077323 Final terms of rows of A077321.

Original entry on oeis.org

2, 5, 19, 41, 101, 103, 337, 353, 433, 461, 991, 673, 1301, 1163, 1801, 1873, 3061, 2053, 4219, 3121, 4159, 3301, 5659, 4153, 6151, 5981, 8263, 6329, 10267, 6361, 14323, 9697, 11287, 10303, 14281, 10729, 19759, 14593, 17863, 15761, 22961, 14407
Offset: 1

Views

Author

Amarnath Murthy, Nov 04 2002

Keywords

Crossrefs

Cf. A077321, A077322, A077324, A077325.

Programs

  • Maple
    A077323 := proc(nmax) local n,a,T,i,p ; T := [] ; a := [] ; n :=1 ; while nops(a) < nmax do for i from 1 to n do p := 2 ; while ( p in T ) or (p-1) mod n <> 0 do p := nextprime(p) ; od ; T := [op(T),p] ; if i = n then a := [op(a),p] ; fi ; od ; n := n+1 ; od ; RETURN(a) ; end: A077323(50) ; # R. J. Mathar, Feb 03 2007
  • Mathematica
    nrows = 42;
A077321[nmax_] := Module[{n = 1, a = {}, i, p}, While[Length[a] < nmax, For[i = 1, i <= n, i++, p = 2; While[MemberQ[a, p] || Mod[p - 1, n] != 0, p = NextPrime[p]]; a = Append[a, p]]; n = n + 1]; Return[a]];
T = A077321[nmax = nrows (nrows + 1)/2];
a[n_] := T[[n (n + 1)/2]];
Table[a[n], {n, 1, nrows}] (* Jean-François Alcover, May 30 2023, after R. J. Mathar *)

Extensions

Corrected and extended by R. J. Mathar, Feb 03 2007

A077324 Sum of terms of n-th row of A077321.

Original entry on oeis.org

2, 8, 39, 124, 275, 462, 1505, 1816, 2439, 3080, 7271, 5256, 10725, 11284, 18435, 20336, 33031, 24984, 45201, 42120, 62937, 52646, 77671, 68544, 110925, 105326, 163161, 120372, 204189, 124710, 260183, 212096, 264165, 251906, 343735, 276624
Offset: 1

Views

Author

Amarnath Murthy, Nov 04 2002

Keywords

Comments

By definition a(n) == 0 (mod n).

Crossrefs

Cf. A077321, A077322, A077323, A077325.

Programs

  • Maple
    A077324 := proc(nmax) local n,a,T,i,p,s ; T := [] ; a := [] ; n :=1 ; while nops(a) < nmax do s := 0 ; for i from 1 to n do p := 2 ; while ( p in T ) or (p-1) mod n <> 0 do p := nextprime(p) ; od ; T := [op(T),p] ; s := s+p ; od ; a := [op(a),s] ; n := n+1 ; od ; RETURN(a) ; end: A077324(50) ; # R. J. Mathar, Feb 03 2007
  • Mathematica
    A077324[nmax_] := Module[{n = 1, a = {}, T = {}, i, p, s}, While[Length[a] < nmax, s = 0; For[i = 1, i <= n, i++, p = 2; While[MemberQ[T, p] || Mod[p - 1, n] != 0, p = NextPrime[p]]; T = Append[T, p]; s = s + p]; a = Append[a, s]; n = n + 1]; Return[a]];
A077324[36] (* Jean-François Alcover, Oct 17 2024, after R. J. Mathar *)

Extensions

Corrected and extended by R. J. Mathar, Feb 03 2007

A077325 Average of terms of n-th row of A077321.

Original entry on oeis.org

2, 4, 13, 31, 55, 77, 215, 227, 271, 308, 661, 438, 825, 806, 1229, 1271, 1943, 1388, 2379, 2106, 2997, 2393, 3377, 2856, 4437, 4051, 6043, 4299, 7041, 4157, 8393, 6628, 8005, 7409, 9821, 7684, 12549, 10233, 12581, 11090, 14249, 9811, 18467, 13616
Offset: 1

Views

Author

Amarnath Murthy, Nov 04 2002

Keywords

Crossrefs

Cf. A077321, A077322, A077323, A077324.

Programs

  • Maple
    A077325 := proc(nmax) local n,a,T,i,p,s ; T := [] ; a := [] ; n :=1 ; while nops(a) < nmax do s := 0 ; for i from 1 to n do p := 2 ; while ( p in T ) or (p-1) mod n <> 0 do p := nextprime(p) ; od ; T := [op(T),p] ; s := s+p ; od ; a := [op(a),s/n] ; n := n+1 ; od ; RETURN(a) ; end: A077325(50) ; # R. J. Mathar, Feb 03 2007

Formula

a(n) = A077324(n)/n.

Extensions

Corrected and extended by R. J. Mathar, Feb 03 2007
Showing 1-4 of 4 results.

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