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 1-3 of 3 results.

A100301 Primes resulting from A085013.

Original entry on oeis.org

5, 17, 107, 1367, 31397, 910457, 33686837, 1448533907, 88360568207, 6450321478967, 574078611627887, 78648769793020247, 11875964238746056997, 1983286027870591518167, 394673919546247712114837
Offset: 1

Views

Author

Herman H. Rosenfeld (herm3(AT)pacbell.net), Dec 29 2004

Keywords

Crossrefs

Cf. A100276. Different from A098028.

Programs

  • Mathematica
    NextPrim[n_] := Block[{k = n + 1}, While[ ! PrimeQ[k], k++ ]; k]; a[0] = 1; a[n_] := a[n] = Block[{p = NextPrim[ a[n - 1]], q = Product[a[i], {i, 0, n - 1}]}, While[ !PrimeQ[p*q + 2], p = NextPrim[p]]; p]; Table[ Product[ a[i], {i, n}] + 2, {n, 16}] (* Robert G. Wilson v, Jan 12 2005 *)

Extensions

More terms from Robert G. Wilson v, Jan 12 2005

A083566 a(1) = 1; for n>1, a(n) = smallest odd number > a(n-1) such that a(1)*...*a(n) + 2 is a prime.

Original entry on oeis.org

1, 3, 5, 7, 9, 15, 19, 25, 27, 53, 57, 65, 71, 87, 101, 151, 195, 247, 253, 255, 277, 289, 291, 301, 321, 355, 361, 443, 455, 461, 491, 531, 533, 541, 599, 603, 619, 635, 647, 667, 805, 817, 871, 1003, 1011, 1179, 1205, 1223, 1327, 1357, 1531, 1551, 1603, 1619
Offset: 1

Views

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 13 2003

Keywords

Links

Crossrefs

Cf. A084723, A084724, A084725, A085013.

Programs

  • Mathematica
    a[1] = 1; a[n_] := a[n] = Block[{k = a[n - 1] + 2}, While[ !PrimeQ[k*Times @@ Table[a[i], {i, 1, n - 1}] + 2], k += 2]; k]; Table[ a[n], {n, 1, 54}]
nxt[{pr_,a_}]:=Module[{k=a+2},While[!PrimeQ[pr k+2],k=k+2];{pr k,k}]; NestList[nxt,{1,1},60][[;;,2]] (* Harvey P. Dale, Jul 10 2023 *)

Extensions

Edited and extended by Robert G. Wilson v, Jun 17 2003
Edited by N. J. A. Sloane, Nov 01 2008 at the suggestion of R. J. Mathar

A100276 a(0)=3; for n > 0, a(n) = smallest prime > a(n-1) such that Product_{i=0..n} a(i) - 2 is prime.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 19, 23, 59, 71, 73, 83, 89, 97, 191, 337, 359, 433, 569, 617, 643, 691, 809, 811, 1439, 1447, 1451, 1553, 1571, 1741, 1993, 2141, 2339, 2477, 2693, 2791, 2887, 2917, 4021, 5039, 5431, 5581, 5857, 6353, 6521, 6529, 6857, 7211, 7591, 7883
Offset: 0

Views

Author

Herman H. Rosenfeld (herm3(AT)pacbell.net), Dec 29 2004

Keywords

Examples

			3*5-2=13 is prime;
3*5*7-2=103 is prime;
3*5*7*11-2=1153 is prime;
3*5*7*11*13-2=15013 is prime.

Links

Crossrefs

See A100277 for the resulting primes. Cf. A085013, A100301.

Programs

  • Mathematica
    nxt[{pr_,a_}]:=Module[{p=NextPrime[a]},While[CompositeQ[pr*p-2],p=NextPrime[p]];{pr*p,p}]; NestList[nxt,{3,3},50][[;;,2]] (* Harvey P. Dale, Mar 30 2024 *)

Extensions

Corrected and extended by Emeric Deutsch, Mar 26 2005
More terms from Ryan Propper, Jan 11 2008
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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