A365022 -id:A365022 - cp's OEIS frontend

A365023 The greater of twin Carmichael numbers: a pair of consecutive Carmichael numbers (A002997) without a non-prime-power weak Carmichael number (A087442) between them.

2821, 63973, 530881, 658801, 670033, 852841, 1050985, 2113921, 4909177, 6049681, 6054985, 8355841, 8719921, 9494101, 9585541, 9613297, 11205601, 11972017, 12262321, 15888313, 17316001, 26932081, 35703361, 36765901, 38637361, 41471521, 43331401, 43620409, 45890209

Offset: 1

Amiram Eldar, Aug 17 2023

nonn

Amiram Eldar, Table of n, a(n) for n = 1..1000
Mauro Fiorentini, Carmichael gemelli (numeri di) (in Italian).
Romeo Meštrović, Generalizations of Carmichael numbers I, arXiv:1305.1867 [math.NT], 2013.

Subsequence of A002997.

Cf. A000961, A087442, A225498, A365022 (lesser counterparts), A365024.

npwcQ[n_] := Length[(p = FactorInteger[n][[;; , 1]])] > 1 && AllTrue[p, Divisible[n - 1, # - 1] &]; (* A087442 *)
seq[nmax_] := Module[{carmichaels = Select[Range[1, nmax, 2], CompositeQ[#] && Divisible[# - 1, CarmichaelLambda[#]] &], s = {}, c1, c2}, Do[c1 = carmichaels[[k]] + 2; c2 = carmichaels[[k + 1]] - 2; While[c1 < c2, If[npwcQ[c1], Break[]]; c1 += 2]; If[c1 == c2, AppendTo[s, carmichaels[[k+1]]]], {k, 1, Length[carmichaels] - 1}]; s]; seq[10^6]

A365024 Starts of runs of 3 consecutive Carmichael numbers (A002997) without a non-prime-power weak Carmichael number (A087442) between any two consecutive members.

Original entry on oeis.org

656601, 5968873, 9582145, 45877861, 67653433, 84311569, 171454321, 171679561, 193708801, 193910977, 230630401, 357277921, 367804801, 393122521, 393513121, 393716701, 395044651, 557160241, 703995733, 710382401, 775368901, 832060801, 833608321, 834244501, 939947009

Offset: 1

Amiram Eldar, Aug 17 2023

nonn

The second member in each triple is a term of both A365022 and A365023.

171454321 is the least start of 4 consecutive Carmichael numbers with this property, and 393122521 is the least start of 5, and also 6, consecutive Carmichael numbers with this property.

Amiram Eldar, Table of n, a(n) for n = 1..214
Amiram Eldar, List of triples.
Mauro Fiorentini, Carmichael gemelli (numeri di) (in Italian).
Romeo Meštrović, Generalizations of Carmichael numbers I, arXiv:1305.1867 [math.NT], 2013.

Subsequence of A002997 and A365023.

Cf. A000961, A087442, A225498, A365022.

npwcQ[n_] := Length[(p = FactorInteger[n][[;; , 1]])] > 1 && AllTrue[p, Divisible[n - 1, # - 1] &]; (* A087442 *)
seq[indmax_] := Module[{carmichaels = Cases[Import["https://oeis.org/A002997/b002997.txt", "Table"], {, }][[;; , 2]], s1 = s2 = {}, c1, c2, i}, Do[c1 = carmichaels[[k]] + 2; c2 = carmichaels[[k + 1]] - 2; While[c1 < c2, If[npwcQ[c1], Break[]]; c1 += 2]; If[c1 == c2, AppendTo[s1, carmichaels[[k]]]; AppendTo[s2, carmichaels[[k + 1]]]], {k, 1, Min[indmax, Length[carmichaels] - 1]}]; i = Position[Rest[s1] - Most[s2], 0] // Flatten; s1[[i]]]; seq[200]

cp's OEIS Frontend

A365023 The greater of twin Carmichael numbers: a pair of consecutive Carmichael numbers (A002997) without a non-prime-power weak Carmichael number (A087442) between them.

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