A181723 -id:A181723 - cp's OEIS frontend

A100208 Minimal permutation of the natural numbers such that the sum of squares of two consecutive terms is a prime.

1, 2, 3, 8, 5, 4, 9, 10, 7, 12, 13, 20, 11, 6, 19, 14, 15, 22, 17, 18, 23, 30, 29, 16, 25, 24, 35, 26, 21, 34, 39, 40, 33, 28, 37, 32, 27, 50, 31, 44, 41, 46, 49, 36, 65, 38, 45, 52, 57, 68, 43, 42, 55, 58, 47, 48, 53, 62, 73, 60, 61, 54, 59, 64, 71, 66, 79, 56, 51, 76, 85, 72

Offset: 1

Reinhard Zumkeller, Nov 08 2004

a(1) = 1 and for n>1: a(n) = smallest m not occurring earlier such that m^2 + a(n-1)^2 is a prime; the primes are in A100209.
Note the same parity of a(n) and n for all terms. [Zak Seidov, Apr 27 2011]
Subsequence s(1..m) is a permutation of the natural numbers 1..m only for m=1,2,3. [Zak Seidov, Apr 28 2011]
All filtering primes (A100209) are distinct because primes of the form 4k+1 have a unique representation as the sum of two squares. [Zak Seidov, Apr 28 2011]

Cf. A100209, A100211, A171964, A181723, A181730 [Zak Seidov, Apr 27 2011].

Cf. A080478, A010051.

import Data.Set (singleton, notMember, insert)
a100208 n = a100208_list !! (n-1)
a100208_list = 1 : (f 1 [1..] $ singleton 1) where
   f x (w:ws) s
     | w `notMember` s &&
       a010051 (x*x + w*w) == 1 = w : (f w [1..] $ insert w s)
     | otherwise                = f x ws s where
-- Reinhard Zumkeller, Apr 28 2011

nn = 100; unused = Range[2, nn]; t = {1}; While[k = 0; While[k++; k <= Length[unused] && ! PrimeQ[t[[-1]]^2 + unused[[k]]^2]]; k <= Length[unused], AppendTo[t, unused[[k]]]; unused = Delete[unused, k]]; t (* T. D. Noe, Apr 27 2011 *)

v=[1];n=1;while(n<100,if(isprime(v[#v]^2+n^2)&&!vecsearch(vecsort(v),n),v=concat(v,n);n=0);n++);v \\ Derek Orr, Jun 01 2015

from sympy import isprime
A100208 = [1]
for n in range(1,100):
    a, b = 1, 1 + A100208[-1]**2
    while not isprime(b) or a in A100208:
        b += 2*a+1
        a += 1
    A100208.append(a) # Chai Wah Wu, Sep 01 2014

a(A100211(n)) = A100211(a(n)) = n.
a(n) = sqrt(A073658(n)).
a(n)^2 + a(n+1)^2 = A100209(n).

A171964 "Late bird" numbers in A100208.

Original entry on oeis.org

4, 7, 11, 6, 14, 15, 17, 18, 16, 24, 26, 21, 28, 32, 27, 31, 36, 38, 45, 43, 42, 47, 48, 53, 54, 59, 56, 51, 63, 67, 70, 69, 78, 87, 81, 74, 89, 91, 90, 84, 94, 75, 93, 98, 107, 110, 111, 104, 105, 116, 115, 108, 120, 99, 123, 128, 125, 114, 126, 121, 137, 138, 132, 143, 141, 139, 134, 131, 144, 149, 155, 142, 153, 147, 159, 164, 161, 170, 171, 169, 167, 152, 165, 178, 173, 168, 162, 188, 187, 183, 185, 186, 181, 201, 206, 192, 205, 207, 213, 198, 217, 194, 219, 221, 210, 227, 214, 224, 225, 226, 234, 229, 239, 231, 237, 243, 245, 216, 228, 252, 247, 241, 249, 259, 246, 256, 261, 260, 263, 242, 267, 270, 262, 253, 281, 276, 269, 264, 271, 284, 285, 286, 294, 290

Offset: 1

Zak Seidov, Nov 19 2010

nonn

Numbers n with property that n = A100208(m) with m > n;

n's are given in the order of their appearances in A100208 (and hence the sequence is not monotone).

Cf. A100208, A181723, A181730.

cp's OEIS Frontend

A100208 Minimal permutation of the natural numbers such that the sum of squares of two consecutive terms is a prime.

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