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A376715 Composite numbers in A265640.

4, 8, 9, 12, 16, 18, 20, 25, 27, 28, 32, 36, 44, 45, 48, 49, 50, 52, 63, 64, 68, 72, 75, 76, 80, 81, 92, 98, 99, 100, 108, 112, 116, 117, 121, 124, 125, 128, 144, 147, 148, 153, 162, 164, 169, 171, 172, 175, 176, 180, 188, 192, 196, 200, 207, 208, 212, 225, 236, 242, 243, 244, 245

Offset: 1

Marc Groz, Oct 02 2024

The first dozen terms match those of A013929; 40 is the smallest number that is not squarefree and therefore in A013929 but whose prime factors cannot be artranged to form a palindrome. Other examples are 54, 56, and 60. On the other hand, the current sequence is a proper subset of both A013929 and A265640.

Note that, like A265640, this is not a base-dependent sequence.

			44 is a term, since 44 = 2*11*2.
52 is a term, since 52 = 2*13*2.
180 is a term, since 180 = 2*3*5*3*2.
676 is a term, since 676 = 2*13*13*2.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Intersection of A002808 and A265640.

Cf. A013929, A265640.

isok(n)=my(f=factor(n)[,2]); vecsum(f)>=2 && #select(e->e%2, f)<=1 \\ Andrew Howroyd, Oct 02 2024

from math import isqrt
from sympy.ntheory.factor_ import core, isprime
def ok(n): return n > 3 and (isqrt(n)**2 == n or (not isprime(n) and isprime(core(n))))
print([k for k in range(1, 246) if ok(k)]) # Michael S. Branicky, Oct 03 2024

A374591 Even numbers that can be written as the sum of two isolated primes (A007510).

Original entry on oeis.org

4, 46, 60, 70, 74, 76, 84, 90, 94, 100, 102, 104, 106, 112, 114, 116, 120, 126, 130, 132, 134, 136, 142, 144, 146, 150, 154, 156, 158, 160, 162, 164, 166, 168, 172, 174, 176, 178, 180, 184, 186, 190, 192, 194, 196, 198, 200, 202, 204, 206, 210, 214, 216, 220

Offset: 1

Marc Groz, Jul 12 2024

nonn

			4 = 2 + 2 is a term, as 2 is the smallest isolated prime.
60 = 23 + 37 is the smallest term that is the sum of two distinct isolated primes.

Cf. A007510.

Lim=220;ip=Select[Prime[Range[Lim]], NoneTrue[#+{2, -2}, PrimeQ]&] ;ipp[a_]:={a,a};Select[Union[Total/@Join[ipp/@ip,Subsets[ip,{2}]]],EvenQ[#]&&#<=Lim&] (* James C. McMahon, Aug 10 2024 *)

A373920 Isolated prime Lucas numbers.

Original entry on oeis.org

2, 47, 2207, 3571, 9349, 3010349, 54018521, 370248451, 6643838879, 5600748293801, 688846502588399, 32361122672259149, 412670427844921037470771, 258899611203303418721656157249445530046830073044201152332257717521, 59242995313457729780510823767354730798286848921481374874264534705573628371

Offset: 1

Marc Groz, Jun 22 2024

nonn

			47 is a term because it is the 6th prime Lucas number (per A005479) and is an isolated prime (per A007510).

Intersection of A005479 and A007510.

Cf. A000032.

More terms from Michael S. Branicky, Jun 23 2024

A372807 Numbers whose American English name has exactly three syllables.

Original entry on oeis.org

11, 17, 21, 22, 23, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 36, 38, 39, 41, 42, 43, 44, 45, 46, 48, 49, 51, 52, 53, 54, 55, 56, 58, 59, 61, 62, 63, 64, 65, 66, 68, 69, 70, 81, 82, 83, 84, 85, 86, 88, 89, 91, 92, 93, 94, 95, 96, 98, 99, 100, 200, 300, 400, 500, 600, 800, 900

Offset: 1

Marc Groz, May 13 2024

There are 107 terms, considering all terms up to 10^66 using English names of large numbers and various conventional extensions thereof (see Wikipedia link), since quadrillion, quintillion, etc. each have three or more syllables themselves. Terms like "one googol" (or possibly "a googol"), "two googol," ..., "twelve googol" are unconventional, hence disallowed. - Michael S. Branicky, May 28 2024

			a(2) = 17 is the second number whose name in American English has exactly three syllables: "seventeen".

Michael S. Branicky, Table of n, a(n) for n = 1..107
Wikipedia, Names of Large Numbers

Cf. A075774, A180961.

# uses function in A075774
print([k for k in range(501) if A075774(k) == 3]) # Michael S. Branicky, May 27 2024

A075774(a(n)) = 3. - Michael S. Branicky, May 27 2024

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A376715 Composite numbers in A265640.

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A374591 Even numbers that can be written as the sum of two isolated primes (A007510).

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A373920 Isolated prime Lucas numbers.

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A372807 Numbers whose American English name has exactly three syllables.

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