A215099 a(0)=0, a(1)=1, a(n) = least k>a(n-1) such that k+a(n-2) is prime.

0, 1, 2, 4, 5, 7, 8, 10, 11, 13, 18, 24, 25, 29, 34, 38, 39, 41, 44, 48, 53, 55, 56, 58, 71, 73, 78, 84, 85, 89, 94, 102, 103, 109, 120, 124, 131, 133, 138, 144, 145, 149, 162, 164, 169, 173, 178, 180, 181, 187, 192, 196, 197, 201

Offset: 0

Author

Alex Ratushnyak, Aug 03 2012

Keywords

• nonn

Comments

For n>0 and (n mod 4)<2, a(n) is odd.

Same definition, but k+a(n-2) is a

Fibonacci number: A006498 except first two terms,

Lucas number: A000045 except first two terms,

Pell number: A089928(n-1),

Jacobsthal number: A215095,

factorial: A215096,

square: A194274,

cube: A215097,

triangular number: A011848(n+2),

oblong number: A215098.

Example of a related sequence definition: a(0)=0, a(1)=1, a(n) = least k>a(n-1) such that k+a(n-2) is a cube.

Links

• Iain Fox, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A062042: a(1) = 2, a(n) = least k>a(n-1) such that k+a(n-1) is a prime.

Cf. A073627, A073628.

Programs

PARI

first(n) = my(res = vector(n, i, i-1), k); for(x=3, n, k=res[x-1]+1; while(!isprime(k+res[x-2]), k++); res[x]=k); res \\ Iain Fox, Apr 22 2019 (corrected by Iain Fox, Apr 25 2019)

Python

from sympy import prime
prpr = 0
prev = 1
for n in range(77):
    print(prpr, end=', ')
    b = c = 0
    while c<=prev:
        c = prime(b+1) - prpr
        b+=1
    prpr = prev
    prev = c