A087597 - OEIS

%I #21 Aug 27 2024 22:17:11

%S 0,1,3,6,10,21,28,36,45,55,66,78,105,171,465,528,561,666,2211,4465,

%T 7503,16836,18336,22791,44850,53628,55278,82621,105111,114003,333336,

%U 427350,828828,2220778,2256750,3136260,3373503,3454506,3927003,5443350,6175855,7552441

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

%C Conjecture: Sequence is infinite.

%H Robert Israel, <a href="/A087597/b087597.txt">Table of n, a(n) for n = 1..100</a>

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

%p q:= n-> issqr(1+8*(l-> parse(cat(0,seq(abs(l[-i]-l[1-i])

%p          , i=2..nops(l)))))(convert(n, base, 10))):

%p select(q, [i*(i+1)/2$i=0..10000])[];  # _Alois P. Heinz_, Jul 27 2024

%o (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

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

%K base,nonn

%O 1,3

%A _Amarnath Murthy_, Sep 18 2003

%E Corrected and extended by _R. J. Mathar_, Nov 19 2006

%E Definition clarified, offset corrected, and terms 0,1,3,6 prepended by _Max Alekseyev_, Jul 27 2024