A138348 Lesser of twin primes such that both twin primes have no bases b, 1 < b < p-1, in which p is a palindrome.

137, 4337, 8291, 9419, 10937, 13757, 19427, 20981, 36011, 38327, 43397, 59441, 71327, 74717, 76871, 90437, 91571, 117239, 120941, 121019, 167021, 181787, 191561, 196871, 197597, 221717, 228881, 239387, 240881, 271277, 279119, 289031

Offset: 1

Author

Robert G. Wilson v, Mar 09 2008

Keywords

• nonn
• base

Comments

Also primes in A016038 which are 2 less than their immediate successors.

Prime index of A138348: {33, 592, 1040, 1165, 1328, 1627, 2201, 2359, 3826, 4046, 4524, 6009, 7060, 7367, 7557, 8756, 8852, ...

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..95

Crossrefs

Cf. A001359, A016038.

Programs

Mathematica

palindromicBases[n_] := Module[{p}, Table[p = IntegerDigits[n, b]; If[p == Reverse[p], {b, p}, Sequence @@ {}], {b, 2, n - 2}]]; lst = {}; Do[ If[ Length@ palindromicBases@ Prime@ n == 0, AppendTo[lst, Prime@n]], {n, 22189}]; lst[[ # ]] & /@ Select[ Range@ Length@ lst - 1, lst[[ # ]] + 2 == lst[[ # + 1]] &]
f[n_] := Block[{k = 2}, While[id = IntegerDigits[n, k]; id != Reverse@ id, k++ ]; k]; lst = {2}; Do[p = Prime@ n; If[ f@p == p - 1, AppendTo[lst, p]; Print@p], {n, 128149}]; lst[[ # ]] & /@ Select[Range@11284, lst[[ # ]] + 2 == lst[[ # + 1]] &]
nbQ[n_]:=NoneTrue[Table[IntegerDigits[n,b],{b,2,n-2}],#==Reverse[#]&] && NoneTrue[ Table[IntegerDigits[n+2,b],{b,2,n}],#==Reverse[#]&]; Select[ Select[Partition[Prime[Range[26000]],2,1],#[[2]]-#[[1]]==2&][[All,1]],nbQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 03 2021 *)