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.

A290652 a(n) = PrimePi(A246033(n)) (where PrimePi = A000720).

Original entry on oeis.org

1, 2, 4, 8, 15, 21, 30, 46, 61, 91, 121, 154, 189, 217, 258, 409, 548, 590, 775, 832, 906, 1227, 1270, 1570, 1847, 2116, 2688, 3607, 3714, 3990, 4483, 4502, 6041, 6045, 8078, 9255, 9833, 12136, 12226, 13208, 14356, 16964, 17511, 18858, 18974, 20476, 23489
Offset: 1

Views

Author

Rémy Sigrist, Aug 08 2017

Keywords

Examples

			A246033(42) = 187477 = prime(16964), hence a(42) = 16964.

Crossrefs

Cf. A000720, A246033.

A385503 Popular primes.

Original entry on oeis.org

2, 3, 5, 7, 13, 19, 23, 31, 43, 47, 73, 83, 109, 113, 199, 283, 467, 661, 773, 887, 1109, 1129, 1327, 1627, 2143, 2399, 2477, 2803, 2861, 2971, 3739, 3931, 3947, 4297
Offset: 1

Views

Author

Peter Munn, Jul 01 2025

Keywords

Comments

McNew says that a prime p is "popular" on an interval [2, k] if no prime occurs more frequently than p as the greatest prime factor (gpf, A006530) of the integers in that interval. - N. J. A. Sloane, Jul 25 2017
Does there exist two popular primes p < q such that q gets popular earlier than p, i.e., such that q is popular (for the first time) on [2,k] but p is not popular on [2,j] for any j < k? - Pontus von Brömssen, Jul 02 2025

Links

Crossrefs

Cf. A006530, A124661, A246033.

A167844 Convex primes.

Original entry on oeis.org

101, 103, 107, 109, 113, 127, 137, 139, 149, 211, 223, 227, 229, 239, 307, 311, 313, 317, 337, 347, 349, 359, 401, 409, 419, 421, 433, 439, 449, 457, 503, 509, 521, 523, 547, 557, 569, 601, 607, 613, 617, 619, 631, 643, 647, 659, 701, 709, 719, 727, 733, 739
Offset: 1

Views

Author

Omar E. Pol, Nov 13 2009

Keywords

Comments

Primes in A135641.
Primes whose structure of digits represents a convex function or a convex object. In the graphic representation the points are connected by imaginary line segments from left to right.
See A246033 for a different notion of "convex prime". - N. J. A. Sloane, Jul 25 2017

Links

Crossrefs

Cf. A134811, A134951, A134971, A135641, A167841, A167842, A167843, A167845, A167846, A167853.
See also A246033.

Programs

  • PARI
    \\ See Links section.

Extensions

More terms from Rémy Sigrist, Dec 15 2018

A127925 Primes p such that 2p < prime(k-i) + prime(k+i) for i=1..k-1, where p=prime(k).

Original entry on oeis.org

3, 7, 19, 23, 43, 47, 73, 109, 113, 199, 283, 293, 313, 317, 463, 467, 503, 509, 523, 619, 661, 683, 691, 887, 1063, 1069, 1109, 1129, 1303, 1307, 1321, 1327, 1613, 1621, 1627, 1637, 1669, 1789, 2143, 2161, 2383, 2393, 2399, 2477, 2731, 2753, 2803, 2861, 2971
Offset: 1

Views

Author

T. D. Noe, Feb 06 2007

Keywords

Comments

One of several sets of "good primes" in section A14 of Guy.
McNew calls these numbers "midpoint convex primes". - Peter Munn, Jul 04 2025

References

  • R. K. Guy, Unsolved Problems in Number Theory, 3rd ed. Springer, 2004.

Links

Crossrefs

Cf. A028388.
A246033 is a subset.
Subset of A124661, A178954.

Programs

  • Mathematica
    t={}; n=1; While[Length[t]<100, n++; p=Prime[n]; i=1; While[i

A319126 Convex hull primes, that is, prime numbers corresponding to the convex hull of PrimePi, the prime counting function.

Original entry on oeis.org

2, 3, 5, 7, 13, 19, 23, 31, 43, 47, 73, 113, 199, 283, 467, 661, 887, 1129, 1327, 1627, 2803, 3947, 4297, 5881, 6379, 7043, 9949, 10343, 13187, 15823, 18461, 24137, 33647, 34763, 37663, 42863, 43067, 59753, 59797, 82619, 96017, 102679, 129643, 130699, 142237
Offset: 1

Views

Author

Jean-François Alcover, Sep 11 2018

Keywords

Comments

"Convex hull of PrimePi" is a short wording for "the upper convex hull of the points {p, PrimePi(p)} for p >= 2".

Examples

			Prime 83 is not member because there exist two primes from the convex hull, namely 47 and 113, such that (PrimePi(83) - PrimePi(47))/(83 - 47) < (PrimePi(113) - PrimePi(83))/(113 - 83).

Links

Crossrefs

Cf. A000720, A124661, A167844, A246033 (a subsequence).

Programs

  • Mathematica
    terms = 42;
pMax = 110000;
a[1] = 2;
a[n_] := a[n] = Module[{}, For[slopeMax = 0; p1 = NextPrime[a[n-1]], p1 <= pMax, p1 = NextPrime[p1], slope = (PrimePi[p1] - PrimePi[a[n-1]])/(p1 - a[n-1]); If[slope > slopeMax, slopeMax = slope; p1Max = p1]]; p1Max];
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 42}]
  • PARI
    lista(nn) = my(c, m, p=2, r, s, t=1); print1(p); for(n=2, nn, c=t; m=0; forprime(q=p+1, oo, c++; if(m0&&sJinyuan Wang, Feb 25 2025

Extensions

More terms from Jinyuan Wang, Feb 25 2025
Showing 1-5 of 5 results.

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