A254897 Define a family of sequences as follows: a(1) and a(2) are prime numbers, then if a(n-2) and a(n-1) have the same parity a(n)=(a(n-2)+a(n-1))/2 and if not a(n)=a(n-2)/2+a(n-1) for a(n-2) even or a(n)=a(n-2)+a(n-1)/2 for a(n-1) even. Start the first sequence with the two smallest prime numbers 2 and 3; in general, start the next sequence with the two smallest prime numbers not present in all preceding sequences; the present sequence lists the initial term of all these sequences.

2, 19, 31, 59, 83, 107, 113, 149, 157, 181, 197, 229, 241, 263, 271, 307, 313, 331, 353, 367, 379, 389, 409, 431, 439, 457, 487, 499, 541, 569, 577, 593, 601, 617, 647, 661, 719, 733, 751, 809, 823, 853, 859, 877, 883, 911, 937, 953, 977, 997, 1019

Offset

1,1

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000

Example

a(1)=2, the first term of the sequence A254498.
a(2)=19, the first term of the sequence A254330.
a(3)=31, the smallest prime number not present in A254498 and A254330, and the next one is 37, 31 and 37 starts the third sequence define by the rule, and so on.

Crossrefs

Cf. A254498, A254330.

Sequence in context: A006962 A261312 A090819 * A059697 A103058 A161442

Adjacent sequences: A254894 A254895 A254896 * A254898 A254899 A254900

Keyword

nonn

Author

Pierre CAMI, Feb 10 2015

Status

approved