A012885 -id:A012885 - cp's OEIS frontend

A253386 Suffixes of 3991687693967 (left-truncatable prime).

7, 67, 967, 3967, 93967, 693967, 7693967, 87693967, 687693967, 1687693967, 91687693967, 991687693967, 3991687693967

Offset: 1

Mikk Heidemaa, Dec 31 2014

3991687693967 (13 digits) includes the longest (7 digits) palindromic prime suffix (7693967) among the left-truncatable primes (digit '0' excluded). The largest one (24 digits, see A253427) contains a nonprime palindrome of 7 digits (1264621). The terms from a(3) to a(13) cannot be written as a sum of 3 squares.

			Triangular form:
----------------
............7
...........67
..........967*
.........3967
........93967
.......693967
......7693967**
.....87693967
....687693967
...1687693967
..91687693967
.991687693967
3991687693967***
----------------
* None from 3rd row (967,...,3991687693967) cannot be written as a sum of 3 squares.
** The palindromic prime suffix.
*** a^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g * h * i = 3991687693967;
a=693967; b=93967; c=3967; d=967; e=67; f=7; g=4114278523; h=37; i=27.
a^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g * h * i = 3991687693967^5;
a=693967; b=93967; c=3967; d=967; e=67; f=7;
g=3571123727278334614405609468109056139549629; h=228288322626423; i=124339.
(All primes.)

Mikk Heidemaa, Related material (2015)
Eric Weisstein's World of Mathematics, Truncatable Prime
Wikipedia, Truncatable prime
Index entries for sequences related to truncatable primes

Cf. A012885, A024785, A253427.

Column[ Table[ Mod[ 3991687693967, 10^n], {n, 13}], Right] (* Mikk Heidemaa, Oct 07 2017 *)

a(n) = 3991687693967 mod 10^n for 1 <= n <= 13. - Mikk Heidemaa, Oct 07 2017

A253427 Number of left-truncatable n-digit primes with least significant digit 7.

Original entry on oeis.org

1, 5, 17, 47, 89, 150, 199, 238, 264, 257, 230, 181, 139, 117, 70, 46, 33, 19, 11, 5, 5, 4, 3, 1

Offset: 1

Mikk Heidemaa, Dec 31 2014

Number of n-digit (n <= 24) truncatable primes (i.e., left-truncatable with the least significant digit 7; only prime suffixes without digit '0'). Formed by successively prepending a digit (1,...,9) to the most significant digit (1st is 7) while preserving primality; a(13) with 139 members includes A253386 (includes the palindromic prime suffix 7693967), but a(24) includes just a single one, 357686312646216567629137 (contains the nonprime palindrome 1264621).

			a(1)=1 {7};
a(2)=5 {17,37,47,67,97};
...
a(23)=3 {57686312646216567629137, 95918918997653319693967, 96686312646216567629137};
a(24)=1 {357686312646216567629137}; see also A012885.

I. O. Angell and H. J. Godwin, On Truncatable Primes, Math. Comput. 31, 265-267, 1977.
Eric Weisstein's World of Mathematics, Truncatable Prime
Wikipedia, Truncatable prime
Index entries for sequences related to truncatable primes

Cf. A012885, A024785, A050987, A253386.

S[1]:= {7}:
for n from 2 while nops(S[n-1]) > 0 do
  S[n]:= select(isprime, {seq(seq(i*10^(n-1)+s, i=1..9),s = S[n-1])})
od:
seq(nops(S[i]),i=1..n-2); # Robert Israel, Jan 01 2015

cp's OEIS Frontend

A253386 Suffixes of 3991687693967 (left-truncatable prime).

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