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 1-5 of 5 results.

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}

A129473 Primes p of Erdos-Selfridge class 5+ with largest prime factor of p+1 not of class 4+.

Original entry on oeis.org

15913, 18541, 22921, 36353, 47741, 49201, 52267, 55333, 60589, 64969, 66137, 66721, 69203, 72707, 73291, 74167, 75773, 78401, 79861, 80737, 82051, 84533, 90227, 90373, 95191, 95483, 95629, 97673, 99133, 101323, 103951, 104681, 104827
Offset: 1

Views

Author

M. F. Hasler, Apr 17 2007

Keywords

Comments

See A129470

Examples

			a(1) = 15913 = -1+2*73*109 is a prime of class 5+ since 73 is of class 4+, but the largest divisor of 15913+1 is 109 which is only of class 2+.

Crossrefs

Subsequence of A129470; see also A129471-A129472, A129477-A129478, A129469, A005113, A005105-A005108, A081633.

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])}; A129473(n=100,p=1,a=[])={ local(f); while( #a 3 & 4 > class(f[ #f]), f=factor(1+p=nextprime(p+1))[,1]); forstep( i=#f-1,2,-1, if( 5 < f[1] = max( f[1],1+class( f[i] )), next(2))); if( f[1] == 5, a=concat(a,p); /*print(#a," ",p)*/)); 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}

A129472 Primes p of Erdos-Selfridge class 4+ with largest prime factor of p+1 not of class 3+.

Original entry on oeis.org

3181, 4513, 4957, 6067, 7177, 8731, 9397, 10433, 13171, 14947, 15761, 17389, 19387, 19609, 22051, 22273, 22453, 22717, 23531, 23753, 24197, 26161, 27823, 28711, 37369, 37591, 38183, 38923, 39293, 40993, 41143, 42697, 43067, 44621, 44843
Offset: 1

Views

Author

M. F. Hasler, Apr 17 2007

Keywords

Comments

See A129470

Examples

			a(1) = 3181 = -1+2*37*43 is a prime of class 4+ since 37 is of class 3+, but the largest divisor of 3181+1 is 43 which is only of class 2+.

Crossrefs

Subsequence of A129470; see also A129471, A129473, A129477-A129478, A129469, A005113, A005105-A005107.

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])}; A129472(n=100,p=1,a=[])={ local(f); while( #a 3 & 3 > class(f[ #f]), f=factor(1+p=nextprime(p+1))[,1]); forstep( i=#f-1,2,-1, if( 4 < f[1] = max( f[1],1+class( f[i] )), next(2))); if( f[1] == 4, a=concat(a,p); /*print(#a," ",p)*/)); a}
Showing 1-5 of 5 results.

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