A162930 Primes that can be written as a sum of a positive square and a positive cube in more than one way.

17, 89, 233, 449, 577, 593, 1289, 1367, 1601, 1753, 2089, 2521, 3391, 4481, 4721, 5953, 6121, 6427, 7057, 7577, 8081, 9649, 10313, 10657, 10729, 11969, 12329, 13121, 13457, 15137, 15193, 15641, 15661, 16033, 16649, 18523, 21673, 21961, 23201

Offset

1,1

Comments

A subset of these, 2089, 4481, 7057, 15193, 15641, etc., allows this representation in more than two ways (See A206606).

Links

David A. Corneth, Table of n, a(n) for n = 1..10808 (first 500 terms from Seiichi Manyama, terms <= 8*10^7)

Formula

A000040 INTERSECT A054402.

Example

The prime 17 can be written 1^3 + 4^2 as well as 2^3 + 3^2.

Maple

isA162930 := proc(n) if isprime(n) then wa := 0 ; for y from 1 to n/2 do if issqr(n-y^3) then if n -y^3 > 0 then wa := wa+1 ; fi; fi; od: RETURN( wa>1) ; else false; fi; end:
for i from 1 to 2700 do if isA162930 ( ithprime(i)) then printf("%d, ", ithprime(i)) ; fi; od: # R. J. Mathar, Jul 21 2009

Mathematica

lst={}; Do[Do[AppendTo[lst, n^2+m^3], {n, 2*5!}], {m, 2*5!}]; lst=Sort[lst]; lst2={}; Do[If[lst[[n]]==lst[[n+1]]&&PrimeQ[lst[[n]]], AppendTo[lst2, lst[[n]]]], {n, Length[lst]-1}]; lst2;

Prog

(PARI) upto(n) = {my(res = List(), v = vector(n), i, j, i2); for(i = 1, sqrtint(n), i2 = i^2; for(j = 1, sqrtnint(n - i^2, 3), v[i2 + j^3]++)); forprime(p = 2, n, if(v[p] > 1, listput(res, p))); kill(v); res} \\ David A. Corneth, Jun 20 2023

Crossrefs

Cf. A000040, A054402, A123364, A123388, A173795, A206606.

Sequence in context: A282378 A248400 A139947 * A138338 A267820 A200670

Adjacent sequences: A162927 A162928 A162929 * A162931 A162932 A162933

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 17 2009

Extensions

Slightly edited by R. J. Mathar, Jul 21 2009

Status

approved