OFFSET

1,2

COMMENTS

This is not a permutation of the integers > 0 as no square > 4 will appear. Two prime terms can form a pair (2 and 7 for instance) but at least one term must be prime [the pair (1, 3) is ok].

LINKS

Michael De Vlieger, Annotated log-log scatterplot of a(n), n = 1..10^4, showing records in red, numbers entering late in blue, highlighting primes in green, fixed points in gold, and composite prime powers in magenta.

EXAMPLE

The earliest pairs with their square sum: (1, 3) = 4, (2, 7) = 9, (4, 5) = 9, (6, 19) = 25, (8, 17) = 25, (10, 71) = 81, (11, 14) = 25, (12, 13) = 25, etc.

MATHEMATICA

nn = 10^4; c[_] = 0; a[1] = c[1] = 1; u = 2; Do[k = u; If[EvenQ[i], While[Nand[c[k] == 0, AnyTrue[{#, k}, PrimeQ], IntegerQ@ Sqrt[# + k]] &[a[i - 1]], k++]]; Set[{a[i], c[k]}, {k, i}]; If[k == u, While[Or[c[u] > 0, And[IntegerQ@ Sqrt@ u, u > 4]], u++]], {i, 2, nn}]; Array[a, nn] (* Michael De Vlieger, May 24 2022 *)

CROSSREFS

KEYWORD

nonn

AUTHOR

Eric Angelini and Carole Dubois, May 24 2022

STATUS

approved