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 A308335 Palindromic primes such that sum of digits = number of digits. 1
 11, 10301, 1201021, 3001003, 10000900001, 10002520001, 10013131001, 10111311101, 10301110301, 11012121011, 11020302011, 11030103011, 11100500111, 11120102111, 12000500021, 12110101121, 13100100131, 30000500003, 30011111003, 1000027200001, 1000051500001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Every palindrome with an even number of digits is divisible by 11, so 11 is the only term of the sequence with an even number of digits. Every palindrome with a number of digits which is a multiple of 3 also has a sum of digits which is divisible by 3, so there is no term with 3*k digits. So, except 11 with 2 digits, the terms of this sequence must have a number of digits that belongs to A007310. For n > 1, the middle digit of a(n) is odd. - Chai Wah Wu, Jun 30 2019 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 G. L. Honaker, Jr. and Chris Caldwell, Prime Curios!, 10201021. EXAMPLE 3001003 is a term because it is a palindromic prime that has 7 digits and its sum of its digits is 7. MATHEMATICA f[n_] := If[n==2, {11}, If[Mod[(n-1) (n-5), 6]>0, {}, Block[{h = (n - 1)/2, L={}, p}, Do[p = Select[ Flatten[ Permutations /@ IntegerPartitions[ (n - c)/2, {h}, Range[0, 9]], 1], MemberQ[{1, 3, 7, 9}, Last[#]] &]; L = Join[L, Select[ FromDigits /@ (Flatten[{Reverse[#], c, #}] & /@ p), PrimeQ]], {c, 1, n-2, 2}]; Sort[L]]]]; Join @@ (f /@ Range[13]) (* Giovanni Resta, Jun 06 2019 *) PROG (PARI) isok(p) = isprime(p) && (d=digits(p)) && (Vecrev(d) == d) && (#d == vecsum(d)); \\ Michel Marcus, Jun 29 2019 CROSSREFS Intersection of A000040 (primes), A002113 (palindromes) and A061384 (sum of digits = number of digits). Intersection of A002385 and A061384. Intersection of A069710 and A002113. Sequence in context: A157709 A267815 A121520 * A083442 A114120 A118557 Adjacent sequences: A308332 A308333 A308334 * A308336 A308337 A308338 KEYWORD nonn,base AUTHOR Bernard Schott, May 20 2019 EXTENSIONS a(6)-a(21) from Jon E. Schoenfield, May 20 2019 STATUS approved

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Last modified April 12 07:22 EDT 2024. Contains 371623 sequences. (Running on oeis4.)