A344871 a(n) is the least number that can be represented in exactly n ways as the sum of a prime and its digit reversal.

1, 4, 44, 88, 1090, 3212, 4334, 2992, 5995, 4994, 7997, 9779, 5104, 11110, 11891, 10109, 11000, 10780, 108880, 110500, 252142, 278872, 296692, 293282, 308902, 287782, 411103, 289982, 466664, 281072, 457754, 398893, 298892, 462154, 517814, 494384, 299992, 707806, 471064, 476674, 487784, 467764

Offset

0,2

Comments

If the reversal of p is another prime, p+reversal(p) and reversal(p)+p are both counted.

a(n) is the first number that occurs exactly n times in A061227.

Links

Robert Israel, Table of n, a(n) for n = 0..92

Example

a(4) = 1090 because 1090 = 149+941 = 347+743 = 743+347 = 941+149, and this is the least number with exactly four such representations.

Maple

revdigs:= proc(n) local L, t;
L:= convert(n, base, 10);
add(L[-t]*10^(t-1), t=1..nops(L));
end proc:
V:= Vector(10^6):
p:= 1:
do
  p:= nextprime(p);
  if p > 9*10^5 then break fi;
  r:= p+revdigs(p);
  if r <= 10^6 then V[r]:= V[r]+1 fi
od:
A:= Array(0..64):
for i from 1 to 10^6 do
  if V[i] <= 64 and A[V[i]] = 0 then A[V[i]]:= i fi
od:
convert(A, list);

Crossrefs

Cf. A004086, A061227, A056964.

Sequence in context: A364680 A284065 A063837 * A071125 A193448 A200456

Adjacent sequences: A344868 A344869 A344870 * A344872 A344873 A344874

Keyword

nonn,base

Author

J. M. Bergot and Robert Israel, May 31 2021

Status

approved