A365023 -id:A365023 - cp's OEIS frontend

A365022 The lesser of twin Carmichael numbers: a pair of consecutive Carmichael numbers (A002997) without a non-prime-power weak Carmichael number (A087442) between them.

2465, 62745, 512461, 656601, 658801, 838201, 1033669, 2100901, 4903921, 5968873, 6049681, 8341201, 8719309, 9439201, 9582145, 9585541, 11119105, 11921001, 12261061, 15829633, 17236801, 26921089, 35571601, 36121345, 38624041, 41341321, 43286881, 43584481, 45877861

Offset: 1

Amiram Eldar, Aug 17 2023

nonn

The sequence of weak Carmichael numbers is A225498. The weak Carmichael numbers that are not powers of primes (A000961) are in A087442.

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, A365023 (greater 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]]]], {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

A365022 The lesser 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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