A100208 -id:A100208 - cp's OEIS frontend

A272878 a(0) = a(1) = 1, smallest a(n+1) > a(n-1) such that a(n)^2 + a(n+1)^2 is prime.

1, 1, 2, 3, 8, 5, 16, 9, 26, 11, 30, 13, 32, 15, 34, 21, 44, 29, 46, 39, 50, 43, 60, 61, 64, 71, 66, 79, 74, 81, 100, 83, 102, 95, 104, 101, 114, 109, 134, 115, 136, 135, 146, 139, 154, 141, 160, 143, 168, 155, 172, 165, 178, 173, 190, 177, 200, 189, 206, 199

Offset: 0

Thomas Ordowski, May 08 2016

The associated primes 2, 5, 13, 73, 89, 281, 337, 757, 797, ... create a strictly increasing sequence. What is the rate of its growth?

Positive integers that are not in this sequence are 4, 6, 7, 10, 12, 14, 17, 18, 19, 20, 22, 23, 24, 25, 27, ... - Altug Alkan, May 14 2016

Amiram Eldar, Table of n, a(n) for n = 0..10000

Cf. A073658, A080478, A100208.

a[0]=1; a[1]=1; a[n_]:=a[n]= Block[{t = a[n-2] + 1}, While[! PrimeQ[t^2 + a[n-1]^2], t++]; t]; Array[a, 80, 0] (* Giovanni Resta, May 08 2016 *)

lista(nn) = {print1(x = 1, ", "); print1(y = 1, ", "); for (n=2, nn, z = x+1; while (! isprime(y^2+z^2), z++); print1(z, ", "); x = y; y = z;);} \\ Michel Marcus, May 08 2016

More terms from Michel Marcus, May 08 2016

A258743 Fixed points in A055266.

Original entry on oeis.org

1, 4, 6, 9, 12, 13, 14, 18, 21, 24, 25, 26, 29, 33, 36, 39, 42, 43, 44, 47, 48, 51, 54, 57, 58, 59, 60, 61, 62, 63, 66, 67, 68, 72, 73, 74, 78, 81, 84, 85, 86, 89, 93, 94, 95, 99, 102, 103, 104, 105, 108, 109, 110, 111, 114, 117, 118, 119, 123, 124, 125, 128, 131, 134, 138, 141, 144, 145, 146, 149, 150, 151, 152, 153

Offset: 1

Derek Orr, Jun 08 2015

nonn

Numbers n such that A055266(n) = n.

Cf. A100208, A181730.

v=[0]; k=1; while(#v<=10^3, if(!isprime(k+v[#v])&&!vecsearch(vecsort(v), k), v=concat(v, k); if(k==#v-1,print1(k,", ")); k=0); k++);

A258744 Fixed points in A258742.

Original entry on oeis.org

1, 10, 11, 12, 15, 16, 17, 20, 21, 22, 25, 28, 29, 33, 34, 38, 39, 42, 45, 46, 47, 50, 53, 54, 55, 56, 57, 58, 59, 60, 63, 64, 65, 68, 69, 73, 74, 75, 76, 77, 78, 79, 82, 85, 88, 89, 90, 93, 94, 95, 96, 97, 100, 103, 104, 107, 108, 109, 113, 114, 115, 118, 119, 120, 121, 122, 125, 126, 127, 128, 129, 130, 133, 134

Offset: 1

Derek Orr, Jun 08 2015

nonn

Numbers n such that A258742(n) = n.

Cf. A258742, A100208.

print1(1,", ");v=[1]; k=1; while(#v<=200, if(!isprime(k^2+v[#v]^2)&&!vecsearch(vecsort(v), k), v=concat(v, k); if(k==#v, print1(k, ", ")); k=0); k++)

cp's OEIS Frontend

A272878 a(0) = a(1) = 1, smallest a(n+1) > a(n-1) such that a(n)^2 + a(n+1)^2 is prime.

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A258743 Fixed points in A055266.

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A258744 Fixed points in A258742.

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