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

Author

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

Keywords

• nonn
• base

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.

Examples

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

Links

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

Crossrefs

Cf. A004086, A061227, A056964.

Programs

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);