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A087597
Triangular numbers m such that A040115(m) is also triangular.
4
0, 1, 3, 6, 10, 21, 28, 36, 45, 55, 66, 78, 105, 171, 465, 528, 561, 666, 2211, 4465, 7503, 16836, 18336, 22791, 44850, 53628, 55278, 82621, 105111, 114003, 333336, 427350, 828828, 2220778, 2256750, 3136260, 3373503, 3454506, 3927003, 5443350, 6175855, 7552441
OFFSET
1,3
COMMENTS
Conjecture: Sequence is infinite.
LINKS
EXAMPLE
171 is a member as A040115(171) = 66 is also a triangular number.
MAPLE
q:= n-> issqr(1+8*(l-> parse(cat(0, seq(abs(l[-i]-l[1-i])
, i=2..nops(l)))))(convert(n, base, 10))):
select(q, [i*(i+1)/2$i=0..10000])[]; # Alois P. Heinz, Jul 27 2024
PROG
(PARI) dd(k)={ local(kshf, res, dig, odig, p) ; kshf=k ; res=0 ; odig=kshf % 10 ; p=0 ; while(kshf>9, kshf=floor(kshf/10) ; dig=kshf % 10 ; res += 10^p*abs(dig-odig) ; odig=dig ; p++ ; ) ; return(res) ; } isA000217(n)={ if( issquare(1+8*n), return(1), return(0) ) ; } isA087597(n)={ if( isA000217(n) && isA000217(dd(n)), return(1), return(0) ) ; } { for(k=10, 10000000, if(isA087597(k), print1(k, ", ") ; ) ; ) ; } \\ R. J. Mathar, Nov 19 2006
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Sep 18 2003
EXTENSIONS
Corrected and extended by R. J. Mathar, Nov 19 2006
Definition clarified, offset corrected, and terms 0,1,3,6 prepended by Max Alekseyev, Jul 27 2024
STATUS
approved