A380961 Primes prime(k) such that (prime(k) + prime(k+1)) mod (prime(k) - prime(k-1)) != 0.

53, 97, 127, 157, 173, 191, 211, 223, 251, 257, 263, 307, 331, 347, 367, 373, 397, 401, 409, 431, 457, 467, 479, 487, 491, 499, 509, 541, 563, 593, 607, 641, 653, 673, 709, 719, 727, 733, 743, 751, 761, 769, 787, 797, 821, 839, 853, 877, 887, 907, 911, 929, 937, 947, 967, 977, 991, 997, 1009, 1031, 1061, 1069, 1103, 1123

Offset

1,1

Comments

It seems that the proportion of primes in the sequence, among all primes, increases with larger terms (perhaps to the point where almost all primes are terms?).

Links

James C. McMahon, Table of n, a(n) for n = 1..10000

Example

prime(16) = 53 is a term since (53+59) mod (53-47) != 0.
prime(3) = 5 is not a term since (5+7) mod (5-3) = 0.

Mathematica

Select[Prime[Range[2, 188]], Mod[#+NextPrime[#], (#-NextPrime[#, -1])]!=0&] (* James C. McMahon, Feb 23 2025 *)

Crossrefs

Cf. A000040, A001043, A001223.

Sequence in context: A033234 A266845 A238678 * A142296 A180520 A139959

Adjacent sequences: A380958 A380959 A380960 * A380962 A380963 A380964

Keyword

nonn,easy

Author

Najeem Ziauddin, Feb 09 2025

Status

approved