This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
35=5*7 is semiprime and 53 is prime.
a(9)=3 because A260703(9) = 336 and the set of the divisors of 336, {1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336} contains 3 pairs (12, 21), (24, 42) and (48, 84) with the property: 21 = reversal(12), 42 = reversal(24) and 84 = reversal(48).
with(numtheory):nn:=5000:
for n from 1 to nn do:
it:=0:d:=divisors(n):d0:=nops(d):
for i from 1 to d0 do:
dd:=d[i]:y:=convert(dd,base,10):n1:=length(dd):
s:=sum('y[j]*10^(n1-j)', 'j'=1..n1):
for k from i+1 to d0 do:
if s=d[k]
then
it:=it+1:
else fi:
od:
od:
if it>0
then
printf(`%d, `,it):
else fi:
od:
f[n_] := Block[{d = Select[Divisors@n, IntegerLength@# > 1 &], palQ, r}, palQ[x_] := Reverse@ # == # &@ IntegerDigits@ x; r = FromDigits@ Reverse@ IntegerDigits@ # & /@ d; Length@ Select[Intersection[d, r], ! palQ@ # &]/2]; f /@ Range@ 3000 /. 0 -> Nothing (* Michael De Vlieger, Nov 17 2015 *)
a(4)=1008 because the set of the divisors {1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008} contains 4 pairs (12, 21), (24, 42), (36, 63) and (48, 84) with the property 21 = reversal(12), 42 = reversal(24), 63 = reversal(36) and 84 = reversal(48).
with(numtheory):nn:=10^8:
for n from 1 to 16 do:
ii:=0:
for m from 1 to nn while(ii=0) do:
it:=0:d:=divisors(m):d0:=nops(d):
for i from 1 to d0 do:
dd:=d[i]:y:=convert(dd,base,10):n1:=length(dd):
s:=sum('y[j]*10^(n1-j)', 'j'=1..n1):
for k from i+1 to d0 do:
if s=d[k]
then
it:=it+1:
else fi:
od:
od:
if it=n
then
ii:=1:printf("%d %d \n",n,m):
else fi:
od:
od:
nbr(vd) = {nb = 0; for (j=1, #vd, da = vd[j]; rda = eval(concat(Vecrev(Str(da)))); rrda = eval(concat(Vecrev(Str(rda)))); if ((da != rda) && vecsearch(vd,rda) && (da == rrda), nb++);); nb/2;}
a(n) = {k=1; while (nbrp(divisors(k)) != n, k++); k;} \\ Michel Marcus, Dec 27 2015
a(1) = 15*51. a(2) = 26*62. a(3) = 39*93. a(4) is not 51*15 because that has already occurred as a(1). a(4) = 58*85.
336 is in the sequence because the set of its divisors {1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336} contains at least two distinct divisors with the property that the reversal of one is equal to the other. This set contains 3 pairs (12, 21), (24, 42) and (48, 84) with the property 21 = reversal(12), 42 = reversal(24) and 84 = reversal(48).
with(numtheory):nn:=20000:
for n from 1 to nn do:
it:=0:d:=divisors(n):d0:=nops(d):
for i from 1 to d0 do:
dd:=d[i]:y:=convert(dd,base,10):n1:=length(dd):
s:=sum('y[j]*10^(n1-j)', 'j'=1..n1):
for k from i+1 to d0 do:
if s=d[k]
then
it:=it+1:
else fi:
od:
od:
if it>0
then
printf(`%d, `,n):
else fi:
od:
fQ[n_] := Block[{d = Select[Divisors@ n, IntegerLength@ # > 1 &], palQ, r}, palQ[x_] := Reverse@ # == # &@ IntegerDigits@ x; r = FromDigits@ Reverse@ IntegerDigits@ # & /@ d; Length@ Select[Intersection[d, r], ! palQ@ # &] >= 2]; Select[Range@ 1500, fQ] (* Michael De Vlieger, Nov 17 2015 *)
121 is a term because 121 = 11 * 11. 403 is a term because 403 = 13 * 31. 1207 is a term because 1207 = 17 * 71. 2701 is a term because 2701 = 37 * 73.
upto(lim)={my(L=List()); forprime(p=2, sqrtint(lim), my(q=fromdigits(Vecrev(digits(p)))); if(isprime(q) && p*q<=lim, listput(L,p*q))); Set(L)}
a(1) = 2161 because this is prime, and R(A158126(2)) = R(1612) = 2161. a(2) = 39841 because this is prime, and R(A158126(20)) = R(148930) = 039841 which in OEIS form strips away leading zero to become 39841. a(7)is the prime 854431 = R(A158126(16)) = R(134458).
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