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 1-10 of 10 results.

A081633 Class 5+ primes (for definition see A005105).

Original entry on oeis.org

1021, 1321, 1381, 1459, 1877, 2467, 2503, 2657, 2707, 3253, 3313, 3547, 3701, 3733, 3907, 4561, 4817, 4937, 5441, 5443, 5527, 5693, 5839, 5861, 6037, 6131, 6211, 6217, 6277, 6361, 6373, 6569, 6653, 7057, 7243, 7591, 7753, 7817, 7883, 8101, 8123, 8221
Offset: 1

Views

Author

Robert G. Wilson v, Mar 20 2003

Keywords

References

  • R. K. Guy, Unsolved Problems in Number Theory, A18.

Links

Crossrefs

Cf. A005113, A005105, A005106, A005107, A005108, A081634, A081635, A081636, A081637, A081638, A081639.

Programs

  • Maple
    For Maple program see Mathar link in A005105.
  • Mathematica
    PrimeFactors[n_Integer] := Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[n]]; f[n_Integer] := Block[{m = n}, If[m == 0, m = 1, While[ IntegerQ[m/2], m /= 2]; While[ IntegerQ[m/3], m /= 3]]; Apply[Times, PrimeFactors[m] + 1]]; ClassPlusNbr[n_] := Length[ NestWhileList[f, n, UnsameQ, All]] - 3; Prime[ Select[ Range[1040], ClassPlusNbr[ Prime[ # ]] == 5 &]]

A081635 Class 7+ primes.

Original entry on oeis.org

15013, 16333, 22093, 24841, 43321, 49003, 52517, 54721, 62533, 63761, 69061, 69073, 70061, 74597, 75781, 75793, 75913, 82561, 83233, 84673, 87433, 87509, 88793, 91081, 92761, 94321, 98737, 99367, 101641, 105097, 110881, 111973, 114343
Offset: 1

Views

Author

Robert G. Wilson v, Mar 20 2003

Keywords

References

  • R. K. Guy, Unsolved Problems in Number Theory, A18.

Links

Crossrefs

Cf. A005113, A005105, A005106, A005107, A005108, A081633, A081634, A081636, A081637, A081638, A081639.

Programs

  • Maple
    For Maple program see Mathar link in A005105.
  • Mathematica
    PrimeFactors[n_Integer] := Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[n]]; f[n_Integer] := Block[{m = n}, If[m == 0, m = 1, While[ IntegerQ[m/2], m /= 2]; While[ IntegerQ[m/3], m /= 3]]; Apply[Times, PrimeFactors[m] + 1]]; ClassPlusNbr[n_] := Length[ NestWhileList[f, n, UnsameQ, All]] - 3; Prime[ Select[ Range[10820], ClassPlusNbr[ Prime[ # ]] == 7 &]]

A081638 Class 10+ primes.

Original entry on oeis.org

1065601, 2424973, 5114881, 7222561, 8124481, 8524091, 8647411, 8650321, 9190681, 9287521, 9590417, 10617601, 10929817, 11996161, 12349093, 12508081, 12786181, 12971117, 13570681, 14113027, 14308123, 14312743, 14476807
Offset: 1

Views

Author

Robert G. Wilson v, Mar 20 2003

Keywords

References

  • R. K. Guy, Unsolved Problems in Number Theory, A18.

Links

Crossrefs

Cf. A005113, A005105, A005106, A005107, A005108, A081633, A081634, A081635, A081636, A081637, A081639.

Programs

  • Maple
    For Maple program see Mathar link in A005105.
  • Mathematica
    PrimeFactors[n_Integer] := Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[n]]; f[n_Integer] := Block[{m = n}, If[m == 0, m = 1, While[ IntegerQ[m/2], m /= 2]; While[ IntegerQ[m/3], m /= 3]]; Apply[Times, PrimeFactors[m] + 1]]; ClassPlusNbr[n_] := Length[ NestWhileList[f, n, UnsameQ, All]] - 3; Prime[ Select[ Range[150000], ClassPlusNbr[ Prime[ # ]] == 10 &]]

A081636 Class 8+ primes.

Original entry on oeis.org

49681, 109441, 120103, 151561, 198733, 210193, 246241, 255043, 266401, 280243, 295873, 326659, 326701, 347773, 355171, 360421, 368881, 397633, 397673, 423001, 441877, 447137, 471241, 480541, 489989, 499397, 508037, 511507, 532757, 539401
Offset: 1

Views

Author

Robert G. Wilson v, Mar 20 2003

Keywords

References

  • R. K. Guy, Unsolved Problems in Number Theory, A18.

Links

Crossrefs

Cf. A005113, A005105, A005106, A005107, A005108, A081633, A081634, A081635, A081637, A081638, A081639.

Programs

  • Maple
    For Maple program see Mathar link in A005105.
  • Mathematica
    PrimeFactors[n_Integer] := Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[n]]; f[n_Integer] := Block[{m = n}, If[m == 0, m = 1, While[ IntegerQ[m/2], m /= 2]; While[ IntegerQ[m/3], m /= 3]]; Apply[Times, PrimeFactors[m] + 1]]; ClassPlusNbr[n_] := Length[ NestWhileList[f, n, UnsameQ, All]] - 3; Prime[ Select[ Range[44535], ClassPlusNbr[ Prime[ # ]] == 8 &]]

A081637 Class 9+ primes.

Original entry on oeis.org

532801, 710341, 720617, 1212487, 1261157, 1372081, 1457293, 1490429, 1532173, 1657801, 1788547, 1789093, 1809601, 1829293, 1887877, 1944181, 1960141, 1997587, 2121853, 2161853, 2474413, 2484049, 2557441, 2578801, 2613607
Offset: 1

Views

Author

Robert G. Wilson v, Mar 20 2003

Keywords

References

  • R. K. Guy, Unsolved Problems in Number Theory, A18.

Links

Crossrefs

Cf. A005113, A005105, A005106, A005107, A005108, A081633, A081634, A081635, A081636, A081638, A081639.

Programs

  • Maple
    For Maple program see Mathar link in A005105.
  • Mathematica
    PrimeFactors[n_Integer] := Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[n]]; f[n_Integer] := Block[{m = n}, If[m == 0, m = 1, While[ IntegerQ[m/2], m /= 2]; While[ IntegerQ[m/3], m /= 3]]; Apply[Times, PrimeFactors[m] + 1]]; ClassPlusNbr[n_] := Length[ NestWhileList[f, n, UnsameQ, All]] - 3; Prime[ Select[ Range[196000], ClassPlusNbr[ Prime[ # ]] == 9 &]]

A084071 Class 12+ primes.

Original entry on oeis.org

68198461, 115084901, 138358573, 156811273, 213397621, 220576331, 234432217, 260050573, 282261961, 290996753, 330864497, 353653063, 371500819, 383616341, 406915273, 426240379, 445800983, 446707201, 449558323, 460339577, 472782553
Offset: 1

Views

Author

Robert G. Wilson v, Mar 20 2003

Keywords

References

  • R. K. Guy, Unsolved Problems in Number Theory, A18.

Links

Crossrefs

Cf. A005113, A005105, A005106, A005107, A005108, A081633, A081634, A081635, A081636, A081637, A081638, A081639.

Programs

  • Maple
    For Maple program see Mathar link in A005105.
  • Mathematica
    PrimeFactors[n_Integer] := Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[n]]; f[n_Integer] := Block[{m = n}, If[m == 0, m = 1, While[ IntegerQ[m/2], m /= 2]; While[ IntegerQ[m/3], m /= 3]]; Apply[Times, PrimeFactors[m] + 1]]; ClassPlusNbr[n_] := Length[ NestWhileList[f, n, UnsameQ, All]] - 3; Prime[ Select[ Range[25000000], ClassPlusNbr[ Prime[ # ]] == 12 &]]

A129470 Primes p such that the largest prime factor of p+1 has Erdős-Selfridge class+ < N-1 if p is of class N+.

Original entry on oeis.org

883, 1747, 2417, 2621, 3181, 3301, 3533, 3571, 3691, 3853, 4027, 4133, 4513, 4783, 4861, 4957, 5303, 5381, 5393, 5563, 5641, 5821, 6067, 6577, 6991, 7177, 7253, 7331, 8059, 8093, 8377, 8731, 8839, 8929, 8969, 9221, 9281, 9397, 9613, 9931
Offset: 1

Views

Author

M. F. Hasler, Apr 16 2007

Keywords

Comments

In practice the class+ of a prime p is most often given by 1 + the class of the largest prime factor of p+1; terms of this sequence are counterexamples to this "rule". Terms of this sequence are at least of class 3+, since primes of class 1+ and 2+ have all prime factors of p+1 of class 1+. Terms a(k) of this sequence are >= -1 + 2*A005113(N-1) * nextprime(A005113(N-1)), where N is the class of a(k).

Examples

			a(3) = 883 = -1 + 2*13*17 is a prime of class 3+ since 13 is of class 2+, but the largest divisor of 883+1 is 17 which is only of class 1+.

Crossrefs

Cf. A005105, A005106, A005107, A005108, A005113, A081633, A081634, A081635, A081636, A081637, A081638, A081639, A084071, A090468, A129469, A129471, A129472, A129473, A129474, A129475, A129477, A129478.

Programs

  • PARI
    class(n,s=1)={n=factor(n+s)[,1];if(n[ #n]<=3,1,for(i=2,#n,n[1]=max(class(n[i],s)+1,n[1]));n[1])}; A129470(n=100,p=1,a=[])={ local(f); while( #a 3, f=factor(1+p=nextprime(p+1))[,1]); forstep( i=#f,2,-1, f[i]=class( f[i] ); if( f[i] > f[ #f], a=concat(a,p); /*print(#a," ",p);*/ break))); a}

A129477 Primes p of Erdos-Selfridge class 6+ with largest prime factor of p+1 not of class 5+.

Original entry on oeis.org

2146141, 2182897, 2954773, 3199813, 3224317, 3285577, 3383593, 3505933, 3555121, 3567373, 3653137, 3775417, 3864037, 4250977, 4298533, 4328053, 4493773, 4504651, 4519981, 4572037, 4647277, 4692637, 4719061, 4726537
Offset: 1

Views

Author

M. F. Hasler, Apr 17 2007

Keywords

Comments

See A129470

Examples

			a(1) = 2146141 = -1+2*1021*1051 = A129469[6] is a prime of class 6+ since 2146141+1 has prime factor 1021=A081633[1]=A005113[5] of class 5+, but the largest prime factor of 2146141+1 is 1051=A005107[65] of class 3+.

Crossrefs

Subsequence of A129470; see also A129471-A129473, A129478, A129469, A005113, A005105-A005108, A081633-A081634.

Programs

  • PARI
    class(n,s=1)={n=factor(n+s)[,1];if(n[ #n]<=3,1,for(i=2,#n,n[1]=max(class(n[i],s)+1,n[1]));n[1])}; a129477(n=100,p=1,a=[])={local(f,a5=A005113[5]);p=max(p,a5*nextprime(a5+1)*2-1); while( #a2 & f[ #f-1] >= a5 & 5 > class(f[ #f]), f=factor(1+p=nextprime(p+1))[,1]); forstep( i=#f-1,2,-1, if( 6 < f[1] = max( f[1],1+class( f[i] )), next(2))); if( f[1] == 6, a=concat(a,p); print(#a," ",p))); a}

A129478 Primes p of Erdos-Selfridge class 7+ with largest prime factor of p+1 not of class 6+.

Original entry on oeis.org

17227801, 18207913, 18592957, 19433053, 19608073, 19678081, 20028121, 20518177, 20658193, 20833213, 21043237, 21218257, 21533293, 21743317, 22128361, 22303381, 23668537, 25068697, 25418737, 25453741
Offset: 1

Views

Author

M. F. Hasler, Apr 17 2007

Keywords

Comments

See A129470

Examples

			a(1) = 17227801 = -1+2*2917*2953 = A129469[7] is a prime of class 7+ since 17227801+1 has prime factor 2917 = A081634[1] = A005113[6] of class 6+, but the largest prime factor of 17227801+1 is 2953 = A005107[175] of class 3+.

Crossrefs

Subsequence of A129470; see also A129471-A129473, A129477, A129469, A005113, A005105-A005108, A081633-A081635.

Programs

  • PARI
    class(n,s=1)={n=factor(n+s)[,1];if(n[ #n]<=3,1,for(i=2,#n,n[1]=max(class(n[i],s)+1,n[1]));n[1])}; a129478(n=100,p=1,a=[])={local(f,a6=A005113[6]);p=max(p,a6*nextprime(a6+1)*2-2); while( #a2 & f[ #f-1] >= a6 & 6 > class(f[ #f]), f=factor(1+p=nextprime(p+1))[,1]); forstep( i=#f-1,2,-1, if( 7 < f[1] = max( f[1],1+class( f[i] )), next(2))); if( f[1] == 7, a=concat(a,p); print(#a," ",p))); a}

A101253 a(n) = n-th prime of Erdős-Selfridge classification n+.

Original entry on oeis.org

2, 19, 113, 617, 1877, 8753, 52517, 255043, 1532173, 9287521, 48499459, 353653063, 2136716521, 18171787987, 111795382441
Offset: 1

Views

Author

Jonathan Vos Post, Dec 16 2004

Keywords

Comments

Diagonalization of the Erdős-Selfridge classification of primes n+. See A101231 for diagonalization of the Erdős-Selfridge classification of primes n-.

Examples

			a(1) = 2 because 2 is the first element of A005105.
a(2) = 19 because 19 is the 2nd element of A005106.
a(3) = 113 because 113 is the 3rd element of A005107.
a(4) = 617 because 617 is the 4th element of A005108.
a(5) = 1877 because 1877 is the 5th element of A081633.
a(6) = 8753 because 8753 is the 6th element of A081634.

References

  • R. K. Guy, Unsolved Problems in Number Theory, A18.

Crossrefs

Cf. A101231, A005105, A005106, A005107, A005108, A081633, A081634, A081635, A081636, A081637, A081638, A081639, A005113, A019268.
Cf. A084071, A090468, A129474, A129475.

Extensions

More terms from David Wasserman, Mar 26 2008
Showing 1-10 of 10 results.

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

Content is available under The OEIS End-User License Agreement.