A226536 Palindromes of length greater than 1 in decimal expansion of e (A001113).

828, 18281, 818, 28182, 8281828, 828, 353, 747, 66, 2662, 77, 757, 99, 999, 99, 959, 595, 66, 9669, 696, 676, 77, 2772, 66, 303, 353, 535, 525, 66, 66, 919, 39193, 0, 30, 99, 181, 66, 0, 33, 595, 323, 232, 434, 94349, 323, 33, 88, 525, 101, 11, 383, 70, 99, 88, 4884, 44, 606, 66, 808, 22

Offset: 1

Author

Reinhard Zumkeller and Robert G. Wilson v, Jun 09 2013

Keywords

• nonn
• base

Comments

Begin with the left (most significant) k digits and sequentially remove the first j leading digits until a palindrome is found; continue.

a(33) is actually '00', a(34) is actually '030' (which should be obvious), a(38) is actually '00'.

If e is normal number then all multidigit palindromes should appear.

Examples

			e = 2.7182818284590452353602874713526624977572470936999595749669676...
a(1) = 828, as the first nontrivial palindrome in E is '828', which appears in the digits 4 through 6.
a(2) = 18281, as the second nontrivial palindrome in E is '18281', which appears in the digits 3 through 7.
Please note that a(1) runs from digits 4-6 whereas a(2) runs from 3-7. This is why a(1) appears before a(2).
		

Links

• Eric W. Weisstein, Normal Number
• Index entries for sequences related to palindromes

Crossrefs

Cf. A001113, A002113, A068046, A099052.

Programs

Mathematica

e = RealDigits[E, 10, 250][[1]]; palQ[n_] := n == Reverse[n]; k = 2; lst = {}; While[k < 251, While[j < k, If[ palQ[ Take[e, {j, k}]], p = FromDigits[Take[e, {j, k}]]; AppendTo[lst, p]; Print[p]]; j++]; k++; j = 1]