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.

A081640 a(n) = n-th prime of class 12- according to the Erdős-Selfridge classification.

Original entry on oeis.org

14920303, 18224639, 24867247, 26532953, 34548443, 38003011, 39800743, 41319599, 41443483, 45604771, 46432667, 47247763, 49734341, 49734493, 49749439, 51591833, 53014667, 55257977, 59681383, 59700749, 60804817
Offset: 1

Views

Author

Robert G. Wilson v, Mar 23 2003

Keywords

Comments

The first 184 resp. 300 terms of A081430 allow us to deduce 44 resp. 84 consecutive terms of this sequence. - M. F. Hasler, Apr 05 2007

Examples

			a(1) = 14920303 = 1+2*A081430(3)*3 is the smallest 12- prime

References

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

Links

Crossrefs

Cf. A005113, A005105, A005106, A005107, A005108, A081633, A081633, A081635, A081636, A081637, A081638.
Cf. A056637, A081430, A081641.

Programs

  • 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]]; ClassMinusNbr[n_] := Length[ NestWhileList[f, n, UnsameQ, All]] - 3; Prime[ Select[ Range[3610000], ClassMinusNbr[ Prime[ # ]] == 12 &]]
  • PARI
    nextclassminus( a, p=1, n=[] )={ while( p, n=concat(n,p); p=0; for( i=1,#a, if( p & 2*a[i] >= p-1, break); for( k=ceil(n[ #n]/2/a[i]),a[ #a]/a[i], if( p & 2*k*a[i] >= p-1, break); if( isprime(2*k*a[i]+1), p=2*k*a[i]+1; break(1+(k==1)); ))));vecextract(n,"^1")}; A081640 = nextclassminus(A081430) \\ M. F. Hasler, Apr 05 2007

Formula

{ a(n) } = { p = 2*m*A081430(k)+1 | k=1,2,...,oo and m=1,2,... such that p is prime and m has no factor of class > 11- } - M. F. Hasler, Apr 05 2007

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 21 2007

A129248 a(n) = n-th prime of class 14- according to the Erdős-Selfridge classification.

Original entry on oeis.org

377982107, 437391349, 716174549, 742922699, 1385934359, 1603768277, 1780127639, 1790436371, 1895437139, 1968261067, 2066951933, 2109424013, 2148523669, 2150787839, 2238778847, 2299583987, 2334899909, 2368121663
Offset: 1

Views

Author

M. F. Hasler, Apr 05 2007, Apr 21 2007

Keywords

Comments

a[1..2] calculated using A081641[1..11]; a[3] <= 716174549.

Links

Crossrefs

Cf. A056637, A081640, A081641, A129249, A129250.

Programs

Formula

{ a(n) } = { p = 2*m*A081641(k)+1 | k=1,2,...,oo and m=1,2,... such that p is prime and m has no factor of class > 13- }

A129250 Primes of Erdős-Selfridge class 16-.

Original entry on oeis.org

22111003847, 25782283783, 34824831403, 42970472971, 44905511759, 45490491349, 52486961911, 54560052479, 55437374381, 65803884467, 66333011539
Offset: 1

Views

Author

M. F. Hasler, Apr 21 2007

Keywords

Comments

Knowledge of a(k), k=1..9 allows us to establish A056637(17) = 1 + 2*a(9) = 110874748763.

Links

Crossrefs

Cf. A056637, A081640, A081641, A129248, A129249.

Programs

  • PARI
    nextclass( a, s=-1, p, n=[] )={ if( !p, p=nextprime(a[ #a]+1)); print("Computing all primes of next class up to ",2*p-s ); for( i=1,#a, for( k=1,p/a[i], if( is/*pseudo*/prime(2*k*a[i]-s), n=concat(n,2*k*a[i]-s); ) ) ); vecsort(n) }; A129250=nextclass(A129249)

Formula

{ a(n) } = { p=1+2*k*A129249(n); n=1,2,3..., k=1,2,3... such that p is prime and k has no factor of class > 15- }.
Showing 1-3 of 3 results.

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

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