A087597 Triangular numbers m such that A040115(m) is also triangular.

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

Author

Amarnath Murthy, Sep 18 2003

Keywords

• base
• nonn

Comments

Conjecture: Sequence is infinite.

Examples

			171 is a member as A040115(171) = 66 is also a triangular number.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000217, A040115, A087598, A087599, A087600.

Programs

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

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

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