A230715 -id:A230715 - cp's OEIS frontend

A230808 Smallest sets of 3 consecutive odd numbers that are primes or pseudoprime (base 2). The initial odd number is listed.

3, 641, 643, 4369, 25759, 33149, 87249, 129917, 157637, 212419, 332947, 451901, 656597, 656599, 831405, 1489665, 1608461, 2113665, 3020357, 3370637, 6212357, 6212359, 19092917, 31880577, 34487597, 38790749, 63560683, 81612105, 84028407, 86559045, 274014885

Offset: 1

Shyam Sunder Gupta, Oct 30 2013

nonn

			641 is in sequence because 641, 643, 645 is a set of 3 consecutive odd number where 645 is pseudoprime base 2 and others are prime.

Shyam Sunder Gupta, Table of n, a(n) for n = 1..5001
Jan Feitsma, Tables of pseudoprimes and related data

Cf. A001567, A230559, A228575, A230668, A230715.

A308086 Carmichael numbers c such that c-4, c-2 and c+2 are primes.

Original entry on oeis.org

656601, 11512252145095521, 35151891169379601, 89283676825965441, 209606994019068801, 584047819872236721, 627126355430628801, 1107574117930742001, 1152431453119654401, 2990125943388676401, 6919232969930803761

Offset: 1

Rick L. Shepherd, May 11 2019

nonn

Subsequence of A287591 (Carmichael numbers that are arithmetic means of cousin primes). Calculated from Amiram Eldar's table in that sequence. The Carmichael numbers here are contained within intervals defined by prime triples of the form (p, p+2, p+6); therefore, for each term, four consecutive odd numbers are prime, prime, Carmichael number (divisible by 3), then prime. None of the terms of A287591 available so far are contained within intervals defined by prime triplets of the form (p, p+4, p+6). Is that possible? If so, is it also possible for a Carmichael number to be immediately preceded and succeeded by twin primes, i.e., to be "contained" in a prime quadruplet? (Such Carmichael numbers would necessarily be multiples of 15.)

			656601 = 3*11*101*197 is a term because 656597 and 656599 are twin primes, 656601 is a Carmichael number, and 656603 is also a prime.

Amiram Eldar, Table of n, a(n) for n = 1..36 (terms below 10^22, calculated using data from Claude Goutier)
Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.

Cf. A002997, A007530, A022004, A022005, A230715, A258801, A287591.

More terms from Amiram Eldar, Jul 02 2019

cp's OEIS Frontend

A230808 Smallest sets of 3 consecutive odd numbers that are primes or pseudoprime (base 2). The initial odd number is listed.

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