A171667 -id:A171667 - cp's OEIS frontend

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.

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

Alex Ratushnyak, Mar 31 2015

nonn

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)

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

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

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

A171668 Fibonacci numbers sandwiched between two numbers having same number of divisors.

Original entry on oeis.org

34, 55, 144, 10946, 46368, 196418, 9227465, 1134903170, 4052739537881, 117669030460994, 420196140727489673, 12200160415121876738, 3928413764606871165730, 22698374052006863956975682, 68330027629092351019822533679447, 13598018856492162040239554477268290

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 14 2009

nonn

Amiram Eldar, Table of n, a(n) for n = 1..70

Cf. A000005, A000045, A005237, A005238, A067889, A171666, A171667.

f[n_]:=Length[Divisors[n]]; lst={};Do[fi=Fibonacci[n];If[f[fi-1]==f[fi+1],AppendTo[lst,fi]],{n,170}];lst

a(15)-a(16) from Amiram Eldar, Aug 08 2024

A171669 Pell numbers sandwiched between two numbers having same number of divisors.

Original entry on oeis.org

12, 5741, 2744210, 15994428, 21300003689580, 723573111879672, 1111984844349868137938112, 293199986221627877463941823267862, 9960168529794442859224531878561050, 27749033099085295754434173207717704165, 66992092050551637663438906713182313772

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 14 2009

nonn

Amiram Eldar, Table of n, a(n) for n = 1..19

Cf. A000005, A000129, A005237, A005238, A067889, A171666, A171667, A171668.

f[n_]:=Length[Divisors[n]]; a=1;b=0;c=0;lst={};Do[c=a+b+c;If[f[c-1]==f[c+1],AppendTo[lst,c]];a=b;b=c,{n,80}];lst

a(8)-a(11) from Amiram Eldar, Aug 08 2024

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula

A171668 Fibonacci numbers sandwiched between two numbers having same number of divisors.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

A171669 Pell numbers sandwiched between two numbers having same number of divisors.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions