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 1-4 of 4 results.

A234853 Indices of primes in A234851.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 15, 16, 18, 19, 20, 22, 26, 27, 29, 30, 34, 35, 37, 40, 44, 46, 48, 50, 53, 54, 55, 59, 60, 61, 62, 68, 76, 79, 80, 81, 85, 89, 91, 94, 96, 99, 100, 102, 110, 111, 112, 117, 122, 123, 125, 126, 134, 138, 139, 141, 144, 147
Offset: 1

Views

Author

M. F. Hasler, Dec 31 2013

Keywords

Crossrefs

Cf. A000040, A000720, A014692, A234850, A234851, A234852, A234695.

Programs

  • PARI
    c=0;for(k=1,1999,isprime(prime(k)-k+1)&&c++&&isprime(k)&&print1(c", "))

A234850 Primes in A014692, i.e., of the form prime(k)-k+1, for some k.

Original entry on oeis.org

2, 2, 3, 7, 11, 29, 43, 53, 61, 73, 97, 139, 149, 179, 223, 283, 313, 349, 373, 461, 467, 491, 541, 599, 619, 659, 727, 787, 859, 907, 911, 919, 941, 1019, 1087, 1091, 1187, 1223, 1249, 1283, 1301, 1321, 1433, 1471, 1481, 1511, 1523, 1543
Offset: 1

Views

Author

M. F. Hasler, Dec 31 2013

Keywords

Comments

The first term is listed twice because A014692(1) = 2-1+1 = A014692(2) = 3-2+1 = 2 both are prime; thereafter the sequence A014692 is strictly increasing, so there is no other duplicate value.

Crossrefs

Cf. A234695.

Programs

  • PARI
    for(k=1,999,isprime(p=prime(k)-k+1)&&print1(p","))

Formula

a(n) = prime(A234851(n)), prime = A000040.

A234852 Indices k of primes p=prime(k) such that prime(p)-p+1 is prime.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 9, 11, 13, 14, 18, 20, 23, 24, 27, 29, 34, 36, 40, 42, 46, 47, 48, 53, 58, 59, 60, 62, 63, 64, 66, 68, 70, 71, 73, 90, 95, 100, 103, 105, 110, 121, 122, 127, 128, 132, 133, 134, 141, 143, 144, 153, 155, 156, 162
Offset: 1

Views

Author

M. F. Hasler, Dec 31 2013

Keywords

Crossrefs

Cf. A000040, A000720, A014692, A234850, A234851.

Programs

  • Mathematica
    Select[Range[200],PrimeQ[Prime[Prime[#]]-Prime[#]+1]&] (* Harvey P. Dale, Jul 14 2024 *)
  • PARI
    for(k=1,999,isprime(prime(p=prime(k))-p+1)&&print1(k","))

Formula

a(n) = PrimePi(A234695(n)), PrimePi = A000720.

A235508 Number of ways to write 2*n = p + q with q > 0 such that p, p*(p+1) - prime(p) and prime(q) - q + 1 are all prime.

Original entry on oeis.org

0, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 3, 4, 1, 2, 5, 4, 4, 2, 3, 3, 6, 1, 3, 5, 4, 3, 4, 3, 2, 4, 4, 3, 5, 3, 4, 4, 3, 3, 4, 4, 5, 4, 1, 2, 6, 1, 3, 4, 3, 5, 6, 1, 2, 4, 2, 4, 2, 1, 3, 7, 3, 3, 6, 4, 5, 6, 2, 3, 7, 3, 5, 4, 6, 4, 8, 3, 5, 2, 6, 4, 6
Offset: 1

Views

Author

Zhi-Wei Sun, Jan 14 2014

Keywords

Comments

Conjecture: a(n) > 0 for all n > 1.

Examples

			a(7) = 1 since 2*7 = 11 + 3 with 11, 11*12 - prime(11) = 101 and prime(3) - 3 + 1 = 3 all prime.
a(19) = 1 since 2*19 = 37 + 1 with 37, 37*38 - prime(37) = 1249 and prime(1) - 1 + 1 = 2 all prime.
a(98) = 1 since 2*98 = 11 + 185 with 11, 11*12 - prime(11) = 101 and prime(185) - 185 + 1 = 919 all prime.

Links

Crossrefs

Cf. A000040, A234695, A234851, A235189, A235330, A235661, A235681.

Programs

  • Mathematica
    p[k_]:=PrimeQ[Prime[k](Prime[k]+1)-Prime[Prime[k]]]
q[m_]:=PrimeQ[Prime[m]-m+1]
a[n_]:=Sum[If[p[k]&&q[2n-Prime[k]],1,0],{k,1,PrimePi[2n-1]}]
Table[a[n],{n,1,100}]
Showing 1-4 of 4 results.

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

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