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.

A177335 List of 4-tuples of twin primes q, p, p+2 and q+2 such that 3*q

Original entry on oeis.org

3, 11, 13, 5, 5, 17, 19, 7, 59, 179, 181, 61, 269, 809, 811, 271, 1949, 5849, 5851, 1951, 2999, 8999, 9001, 3001, 6359, 19079, 19081, 6361, 11489, 34469, 34471, 11491, 11549, 34649, 34651, 11551, 14549, 43649, 43651, 14551
Offset: 1

Views

Author

Juri-Stepan Gerasimov, May 08 2010

Keywords

Links

Crossrefs

Cf. A174920, A176821.

Programs

  • Maple
    A174920:= select(q -> isprime(q) and isprime(q+2) and isprime(3*q+2) and isprime(3*q+4), [3,seq(i,i=5..200000,6)]):
map(t -> (t, 3*t+2, 3*t+4, t+2), A174920); # Robert Israel, May 05 2019

Formula

From Robert Israel, May 05 2019: (Start)
a(4k-3) = A174920(k).
a(4k-2) = 3*A174920(k) + 2.
a(4k-1) = 3*A174920(k) + 4.
a(4k) = A174920(k)+2. (End)

Extensions

Verified and extended by D. S. McNeil, May 10 2010

A256386 Numbers m such that m-2, m-1, m+1, m+2 cannot all be represented in the form x*y + x + y for values x, y with x >= y > 1.

Original entry on oeis.org

2, 3, 4, 5, 8, 11, 59, 1319, 1619, 4259, 5099, 6659, 6779, 11699, 12539, 21059, 66359, 83219, 88259, 107099, 110879, 114659, 127679, 130199, 140759, 141959, 144539, 148199, 149519, 157559, 161339, 163859, 175079, 186479, 204599, 230939, 249539, 267959, 273899, 312839
Offset: 1

Views

Author

Alex Ratushnyak, Mar 31 2015

Keywords

Comments

Indices of terms surrounded by pairs of zeros in A255361.
Conjectures:
1. A255361(a(n)) > 0 for n > 4.
2. All terms > 8 are primes.
3. All terms > 8 are terms of these supersequences: A118072, A171667, A176821, A181602, A181669.
From Lamine Ngom, Feb 12 2022: (Start)
For n > 4, a(n) is not a term of A254636. This means that a(n)-2, a(n)-1, a(n)+1 and a(n)+2 are adjacent terms in A254636.
Number of terms < 10^k: 5, 7, 7, 13, 19, 96, 441, 2552, ...
Conjecture 2 would follow if we establish the equivalence "t is in sequence" <=> "t is a term of b(n): lesser of twin primes pair p and q such that (p - 1)/2 and (q + 1)/2 are also a pair of twin primes (A077800)".
It appears that b(n) = a(n) for n > 5. Verified for all terms < 10^9. (End)

Examples

			9, 10, 12, 13 cannot be represented as x*y + x + y, where x >= y > 1. Therefore 11 is in the sequence.

Crossrefs

Cf. A255361, A254636.
Cf. A118072, A171667, A176821, A181602, A181669.
Cf. A001097, A001359, A006512, A077800, A158870.

Formula

a(n) = A158870(n-5) - 2, n > 5 (conjectured). - Lamine Ngom, Feb 12 2022

A177433 List of 4-tuples of twin primes q, p, p+2 and q+2 such that 3*q < 2*p < 2*(p+2) < 3*(q+2).

Original entry on oeis.org

3, 5, 7, 5, 11, 17, 19, 13, 71, 107, 109, 73, 179, 269, 271, 181, 347, 521, 523, 349, 1427, 2141, 2143, 1429, 2111, 3167, 3169, 2113, 3767, 5651, 5653, 3769, 5879, 8819, 8821, 5881, 10091, 15137, 15139, 10093, 10427, 15641, 15643, 10429, 11351, 17027, 17029
Offset: 1

Views

Author

Juri-Stepan Gerasimov, May 08 2010

Keywords

Examples

			a(1)=3, a(2)=5, a(3)=7 and a(4)=5 because 3*3 < 2*5 < 2*(5+2) < 3*(3+2), i.e., 9 < 10 < 14 < 15.

Crossrefs

Cf. A176821, A177335.

Programs

  • Maple
    A001359 := proc(n) option remember; if n = 1 then 3; else for a from procname(n-1)+2 by 2 do if isprime(a) and isprime(a+2) then return a; end if; end do: end if; end proc:
isA001359 := proc(n) isprime(n) and isprime(n+2) ; end proc:
for n from 1 to 400 do q := A001359(n) ; for twop from 3*q+1 to 3*q+2 by 2 do p := twop/2 ; if isA001359(p) and twop+2 < 3*q+6 then printf("%d,%d,%d,%d,",q,p,p+2,q+2) ; end if; end do: end do: # R. J. Mathar, May 10 2010

Extensions

More terms from R. J. Mathar and D. S. McNeil, May 10 2010
Showing 1-3 of 3 results.

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