Lyle Blosser - cp's OEIS frontend

A377596 a(n) = (a(n-1) + a(n-2))^5 for n>=2 where a(0) = 0, a(1) = 1.

0, 1, 1, 32, 39135393, 91801604643057285538237803582587890625

Offset: 0

Lyle Blosser, Nov 29 2024

A second quintic Fibonacci sequence; compare to A112980.

a(6) contains 190 digits and is too large to display here.

			a(3) = 32 = (1+1)^5 = A112980(3)^5.

Lyle Blosser, Table of n, a(n) for n = 0..7
Lyle Blosser, Python program to create b-file

Cf. A112980, A308507.

Module[{a, n}, RecurrenceTable[{a[0] == 0, a[1] == 1, a[n] == (a[n-1] + a[n-2])^5}, a, {n, 6}]] (* or *)
A377596[n_] := If[n < 2, n, (A377596[n-1] + A377596[n-2])^5];
Array[A377596, 7, 0] (* Paolo Xausa, Nov 30 2024 *)

a(n) = (a(n-1) + a(n-2))^5.

a(n) = A112980(n)^5.

A349985 Primes of the form (product of 4 consecutive primes) + (sum of the same 4 consecutive primes).

Original entry on oeis.org

227, 1181, 765169, 575772529, 1844619589, 7916858557, 31095441001, 37809636673, 75033373321, 80635078873, 234564891361, 302257557157, 443314943881, 463236781489, 1215371749321, 1347613229509, 1534404944209, 2967342092629, 5573043569437, 6390859845289

Offset: 1

Lyle Blosser, Jan 08 2022

nonn

It is conjectured that this sequence is infinite, and that similar lists of primes can be generated by using any even number of consecutive primes. Specifying 2 consecutive primes results in A096342. However, it should be noted that the percentage of resulting primes (as compared to all numbers generated in this manner) decreases as the number of consecutive primes to consider increases.

			227 is a term since 227 is prime and is generated by (2*3*5*7) + (2+3+5+7).
1181 is a term since 1181 is prime and is generated by (3*5*7*11) + (3+5+7+11).

Lyle Blosser, Table of n, a(n) for n = 1..498

Cf. A096342.

Select[Table[s=NextPrime[p,Range@4-1];Total@s+Times@@s,{p,Prime@Range@300}],PrimeQ] (* Giorgos Kalogeropoulos, Jan 09 2022 *)

A294671 Decimal expansion of the sum of sqrt(2) and sqrt(5) with no positional regrouping.

Original entry on oeis.org

3, 6, 4, 10, 2, 7, 10, 14, 13, 9, 7, 16, 12, 7, 17, 14, 6, 13, 14, 12, 0, 10, 7, 15, 11, 13, 8, 12, 9, 3, 10, 8, 16, 14, 2, 10, 13, 9, 10, 9, 12, 8, 9, 11, 12, 14, 9, 8, 7, 14, 6, 13, 7, 9, 7, 3, 14, 6, 14, 16, 16, 9, 7, 12, 13, 10, 0, 12, 5, 2, 13

Offset: 1

Lyle Blosser, Nov 06 2017

a(n) is the sum of A002193(n) and A002163(n) without "carrying" (regrouping) when sum is greater than 9.

			for n = 8: A002193(8) = 5, A002163(8) = 9 -> a(8) = 14.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A002193, A002163, A073212, A294670.

Total[RealDigits[#, 10, 120][[1]] & /@ {Sqrt@ 2, Sqrt@ 5}] (* Michael De Vlieger, Nov 13 2017 *)

a(n) = A002193(n) + A002163(n).

A294670 Decimal expansion of the sum sqrt(2) + sqrt(5).

Original entry on oeis.org

3, 6, 5, 0, 2, 8, 1, 5, 3, 9, 8, 7, 2, 8, 8, 4, 7, 4, 5, 2, 1, 0, 8, 6, 2, 3, 9, 2, 9, 4, 0, 9, 7, 4, 3, 1, 4, 0, 1, 0, 2, 9, 0, 2, 3, 4, 9, 8, 8, 4, 7, 3, 7, 9, 7, 4, 4, 7, 5, 7, 6, 9, 8, 3, 4, 0, 1, 2, 5, 3, 4, 0, 4, 0, 9, 9, 9, 1, 1, 9, 3, 8, 2, 6

Offset: 1

Lyle Blosser, Nov 06 2017

			3.65028153987288474521086239294...

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A002193 (sqrt(2)), A002163 (sqrt(5)), A172323, A294671.

SetDefaultRealField(RealField(100)); R:= RealField(); Sqrt(2)+Sqrt(5); // G. C. Greubel, Sep 30 2018

evalf(sqrt(2)+sqrt(5),200); # Wesley Ivan Hurt, Nov 07 2017

RealDigits[Sqrt@ 2 + Sqrt@ 5, 10, 120][[1]] (* Michael De Vlieger, Nov 13 2017 *)

default(realprecision, 100); sqrt(2)+sqrt(5) \\ G. C. Greubel, Sep 30 2018

Equals A002193 + A002163.

cp's OEIS Frontend

User: Lyle Blosser

A377596 a(n) = (a(n-1) + a(n-2))^5 for n>=2 where a(0) = 0, a(1) = 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A349985 Primes of the form (product of 4 consecutive primes) + (sum of the same 4 consecutive primes).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A294671 Decimal expansion of the sum of sqrt(2) and sqrt(5) with no positional regrouping.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A294670 Decimal expansion of the sum sqrt(2) + sqrt(5).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula