A235399 Numbers which are the digital sum of the cube of some prime.

8, 9, 10, 17, 19, 26, 28, 35, 37, 44, 46, 53, 55, 62, 64, 71, 73, 80, 82, 89, 91, 98, 100, 107, 109, 116, 118, 125, 127, 134, 136, 143, 145, 152, 154, 161, 163, 170, 172, 179, 181, 188, 190, 197, 199, 206, 208, 215, 217, 224, 226, 233, 235, 242, 244, 251, 253

Offset: 1

Author

Antonio Graciá Llorente, Jan 09 2014

Keywords

• nonn
• base

Comments

A235398 sorted and duplicates removed.

Crossrefs

Cf. A235398, A004164, A007953, A123157.

Programs

Mathematica

Total[IntegerDigits[#]] & /@ (Prime[Range[5000000]]^3) // Union (* The program generates the first 39 terms of the sequence. To generate more, increase the Range constant. *) (* Harvey P. Dale, Sep 19 2021 *)

PARI

list(maxx)={v=List();n=2; while(n<=maxx,q=n^3;summ=sumdigits(q);
if(setsearch(v,summ)<1,listput(v,summ));n=nextprime(n+1));vecsort(v,,8) ;} \\ Bill McEachen, Jan 29 2014

Formula

Conjecture: for n > 4, a(n) = a(n-2) + 9 = A056020(n).

Conjecture: a(n) = (1/4)*(-1)^n*(9*(-1)^n*(2*n-1) + 5), n >= 3. - Bill McEachen, Feb 13 2021

Extensions

a(37)-a(57) from Lars Blomberg, Feb 10 2016