A215098 -id:A215098 - cp's OEIS frontend

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

Alex Ratushnyak, Aug 03 2012

nonn

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.

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

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

Cf. A073627, A073628.

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)

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

A215095 a(0)=0, a(1)=1, a(n) = least k>a(n-1) such that k+a(n-2) is a Jacobsthal number.

Original entry on oeis.org

0, 1, 3, 4, 8, 17, 35, 68, 136, 273, 547, 1092, 2184, 4369, 8739, 17476, 34952, 69905, 139811, 279620, 559240, 1118481, 2236963, 4473924, 8947848, 17895697, 35791395, 71582788, 143165576, 286331153, 572662307, 1145324612, 2290649224, 4581298449, 9162596899

Offset: 0

Alex Ratushnyak, Aug 03 2012

nonn

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),
factorial: A215096,
square: A194274,
cube: A215097,
triangular number: A011848(n+2),
oblong number: A215098,
prime number: A215099.
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.

Cf. A001045, A006498, A089928, A000045.

prpr = 0
prev = 1
jac = [0]*10000
for n in range(10000):
    jac[n] = prpr
    curr = prpr*2 + prev
    prpr = prev
    prev = curr
prpr, prev = 0, 1
for n in range(1, 44):
    print(prpr, end=', ')
    b = c = 0
    while c<=prev:
        c = jac[b] - prpr
        b+=1
    prpr = prev
    prev = c

Conjecture: G.f. (x+2*x^2)/(1-x-x^2-x^3-2*x^4). - David Scambler, Aug 06 2012

cp's OEIS Frontend

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

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