A249405 Numbers such that any two adjacent digits sum to a prime and such that any digit 0,...,9 can be inserted somewhere preserving this property.

411203, 411205, 3202114, 4111203, 4111205, 4112023, 4112025, 5202114, 30211234, 30232114, 30234114, 30252114, 30256114, 32021114, 32032114, 32034114, 32052114, 32056114, 32074114, 32076114, 32112034, 32112074, 32302114, 32502114, 41111203

Offset

1,1

Comments

"Inserted" includes the possibility of appending the digit or prefixing it if nonzero.

A subsequence of A182175.

There are only two terms, a(1)=411203 and a(2)=411205, below 10^6, and six more terms below 10^7, but many 8-digit terms.

Links

M. F. Hasler, Table of n, a(n) for n = 1..124

Example

a(n)=411203 is the least member of A182175 such that each of the digits 0-9 can be inserted somewhere such that another term of A182175 is obtained; e.g., 411203[0], 41[1]1203, 41[2]1203, 4112[3]03, 41[4]1203, 4112[5]03, 41[6]1203, [7]411203, 411203[8], [9]411203.

Prog

(PARI) is(n)={is_A182175(n)||return; n=digits(n); !for(D=0, 9, isprime(n[#n]+D)&&next; D&&isprime(n[1]+D)&&next; for(i=3-!D, #n-1, isprime(n[i-1]+D)&&isprime(n[i]+D)&&next(2)); return)} \\ A digit D=0 may not be prefixed but may be inserted after the first digit (which is irrelevant for digits > 0).

Crossrefs

Sequence in context: A183705 A233995 A182116 * A237676 A307475 A251828

Adjacent sequences: A249402 A249403 A249404 * A249406 A249407 A249408

Keyword

nonn,base

Author

M. F. Hasler, Oct 27 2014

Extensions

Data and b-file corrected thanks to a remark by Hans Havermann, M. F. Hasler, Oct 29 2014

Status

approved