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

Author

Najeem Ziauddin, Feb 09 2025

Keywords

• nonn
• easy

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?).

Examples

			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.
		

Links

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

Crossrefs

Cf. A000040, A001043, A001223.

Programs

Mathematica

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