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A235399
Numbers which are the digital sum of the cube of some prime.
1
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
1,1
COMMENTS
A235398 sorted and duplicates removed.
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
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
a(37)-a(57) from Lars Blomberg, Feb 10 2016
STATUS
approved