A045392 -id:A045392 - cp's OEIS frontend

A140381 Composites of the form 14k + 9.

9, 51, 65, 93, 121, 135, 177, 205, 219, 247, 261, 275, 289, 303, 345, 387, 415, 429, 471, 485, 513, 527, 555, 583, 597, 611, 625, 639, 667, 681, 695, 723, 737, 765, 779, 793, 807, 835, 849, 891, 905, 933, 961, 975, 989, 1003, 1017, 1045, 1059, 1073, 1101, 1115

Offset: 1

Juri-Stepan Gerasimov, Jun 13 2008

Cf. A045392.

[(14*n+9): n in [0..100]|not IsPrime(14*n+9)] // Vincenzo Librandi, Dec 18 2010

Select[14*Range[0,100]+9,CompositeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 28 2018 *)

Edited by R. J. Mathar, Jun 16 2008

A355025 a(1)=2; for n > 1, a(n) is the least new prime such that a(n-1) + a(n) is a multiple of 7.

Original entry on oeis.org

2, 5, 23, 19, 37, 47, 79, 61, 107, 89, 149, 103, 163, 131, 191, 173, 233, 229, 317, 257, 331, 271, 359, 313, 373, 383, 401, 397, 443, 439, 457, 467, 499, 509, 541, 523, 569, 593, 653, 607, 709, 677, 751, 691, 821, 719, 863, 733, 877, 761

Offset: 1

Zak Seidov, Jun 15 2022

nonn

			2 + 3 = 5 is not a multiple of 7, but 2 + 5 = 7 is, so a(2) = 5.
5 + 2 = 7 is a multiple of 7, but 2 is already a term; 5 + 3 = 8, 5 + 7 = 12, ..., 5 + 19 = 24 are not multiples of 7, but 5 + 23 = 28 is, so a(3) = 23.
23 + 5 = 28 is a multiple of 7, but 5 is already a term; 19 is the next prime p such that 7 divides 23 + p, so a(4) = 19.

Cf. A045392, A045458.

s = {2}; Do[p = 3; a = s[[-1]]; While[MemberQ[s, p] || Mod[a + p, 7] != 0, p = NextPrime[p]]; AppendTo[s, p], {100}]; s

a(n) = A045392((n+1)/2) if n is odd, A045458(n/2) if n is even. - Jon E. Schoenfield, Jun 15 2022

cp's OEIS Frontend

A140381 Composites of the form 14k + 9.

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