A077798 Palindromic wing primes (a.k.a. near-repdigit palindromic primes) of the general form r*(10^d - 1)/9 + (m-r)*10^floor(d/2) where d is the number of digits (an odd number > 1), r is the repeated digit, and m (different from r) is the middle digit.

101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 11311, 11411, 33533, 77377, 77477, 77977, 1114111, 1117111, 3331333, 3337333, 7772777, 7774777, 7778777, 111181111, 111191111, 777767777, 77777677777, 99999199999, 1111118111111

Offset

1,1

Comments

Prime versus probable prime status and proofs are given in the author's table.

References

C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Links

Jon E. Schoenfield, Table of n, a(n) for n = 1..124

Patrick De Geest, PWP Reference Table

Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.

Prog

(Magma) a:=[]; for d in [3..13 by 2] do for r in [1..9] do for m in [0..9] do if m ne r then t:=r*((10^d-1) div 9) + (m-r)*10^(d div 2); if IsPrime(t) then a[#a+1]:=t; end if; end if; end for; end for; end for; a; // Jon E. Schoenfield, Nov 04 2018

Crossrefs

Cf. A077775-A077797.

Sequence in context: A052086 A154270 A056730 * A089360 A056728 A085112

Adjacent sequences: A077795 A077796 A077797 * A077799 A077800 A077801

Keyword

nonn,base

Author

Patrick De Geest, Nov 16 2002

Extensions

Offset corrected by Arkadiusz Wesolowski, Sep 13 2011

Name edited and one more term added by Jon E. Schoenfield, Nov 03 2018

Status

approved