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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
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
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.)